# Wednesday Seminars

### 2017/2018

### Marcus Sperling (Vienna)

20 December 2017

Å73121 - 13.45

Title: Algebraic properties of the monopole formula.

Abstract: The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional N = 4 gauge theory.

In this talk, I will discuss how the two geometric notions "fan" and "monoid" can be very fruitful for the understanding of the monopole formula.

After a brief reminder of the monopole formula, I will introduce the matter fan and reorganise the monopole formula accordingly. I then discuss the resulting benefits such as:

(1) Explicit expressions for the Hilbert series for any gauge group.

(2) Proof that the order of the pole at t=1 and t → ∞ equals the complex or quaternionic dimension of the Coulomb branch.

(3) Identification of a sufficient set of chiral ring generators.

### Vyacheslav Rychkov (IHES and CERN)

13 December 2017

Å73121 - 14.30

Title: Long-range Ising model as a physical example of non-local CFT.

Abstract: TBA.

### Murad Alim (Hamburg)

12 December 2017

Å73121 - 13.45

Title: Algebraic structure of tt* equations, modularity and topological strings.

Abstract: The tt* equations put forward by Cecotti and Vafa are attached to moduli spaces of N=2 theories in 2 dimensions. When these theories are realized as sigma models into a target manifold X, the tt* equations give the moduli space of X the structure of a special Kähler manifold and generalizations thereof. In this talk, I will discuss an algebraic reformulation of the tt* equations, which is intimately connected to modular forms and their generalizations. For Calabi-Yau threefolds, this algebraic structure of tt* equations provides an algebraic formulation of topological string theory.

### EXTRA - Fabio Apruzzi (Pennsylvania)

12 December 2017

Å73121 - 11.00

Title: Green-Schwarz Automorphisms and 6D SCFTs.

Abstract: All known interacting 6D superconformal field theories (SCFTs) have a tensor branch which includes anti-chiral two-forms and a corresponding lattice of string charges. Automorphisms of this lattice preserve the Dirac pairing and specify discrete global and gauge symmetries of the 6D theory. In this talk I will present the general features of a classification of this automorphism group for 6D SCFTs, and some significative explicit examples. This discrete data determines the geometric structure of the moduli space of vacua. Upon compactification, these automorphisms generate Seiberg-like dualities, as well as additional theories in discrete quotients by the 6D global symmetries. When a perturbative realization is available, these discrete quotients correspond to including additional orientifold planes in the string construction.

### Shamil Shakirov (Harvard)

7 December 2017

Å73121 - 10.00

Title: Mapping class groups and difference operators.

Abstract: We review the representation of SL(2,Z) -- the mapping class group of the torus -- by automorphisms of a simple algebra of difference operators. The algebra, known as spherical double affine Hecke algebra (DAHA) plays an important role in many developments in modern representation theory and mathematical physics. We will define a new algebra which is a direct analogue of spherical DAHA for a genus two surface, and sketch the proof of the corresponding mapping class group action. Time permitting, we will explain the connection to the Reshetikhin-Turaev construction, and possible generalizations to higher genus.

### Carlos Shahabazi (Hannover)

29 November 2017

Å73121 - 13.45

Title: On the spin geometry of M theory.

Abstract: I will present a classification of bundles of weakly faithful Clifford modules over a pseudo-Riemannian manifold (M,g) in terms of Lipschitz structures, obtaining the topological obstruction for their existence. For bundles of irreducible real Clifford modules, I will classify all Lipschitz structures, finding a spinorial structure which to the best of my knowledge is new in the literature. As an application of the previous classification, I will show that in signature (10,1) and under a mild assumption on the existence of a Dirac operator, M theory can be defined on (M,g) if and only if (M,g) is Spin, ruling out the possibility of defining M theory on non orientable manifolds.

### EXTRA - Sourav Sarkar (Humboldt)

28 November 2017

Å3419 - 11.00

Title: Mellin Amplitutes for Fermionic Correlators.

Abstract: We define Mellin amplitudes for the fermion-scalar four point function and the fermion four point function. The Mellin amplitude thus defined has multiple components each associated with a tensor structure. In the case of three spacetime dimensions, we explicitly show that each component factorizes on dynamical poles onto components of the Mellin amplitudes for the corresponding three point functions. The novelty here is that for a given exchanged primary, each component of the Mellin amplitude may in general have more than one series of poles. We present a few examples of Mellin amplitudes for tree-level Witten diagrams and tree-level conformal Feynman integrals with fermionic legs, which illustrate the general properties.

### Benjamin Assel (CERN)

22 November 2017

Å73121 - 13.45

Title: RG flows in 3d N=4 gauge theories.

Abstract: I will present a new approach to study the RG flow in 3d N=4 gauge theories, based on an analysis of the Coulomb branch of vacua. The Coulomb branch is described as a complex algebraic variety and important information about the strongly coupled fixed points of the theory can be extracted from the study of its singularities. I will use this framework to study the fixed points of USp(2N) gauge theories with fundamental matter, revealing some surprising scenarios at low amount of matter.

### Oscar Henriksson

8 November 2017

Å73121 - 13.45

Title: Holographic phases of matter from the top down.

Abstract: Gauge/gravity duality can provide a theoretical handle on exotic phases of matter lacking conventional descriptions. However, there are still open questions regarding the exact interpretation of such holographic phases. I will argue that careful "top-down" studies of known dualities, where the full machinery of supergravity comes into play, are important in making progress on such questions. As an example, I will discuss the computation of correlation functions of both fermionic and bosonic operators in states of finite density ABJM theory; these states are described by black holes in N=8 supergravity. Strict adherence to the top-down framework means that meaningful quantitative comparisons between those computations can be made, and allows one to search for previously unseen correlations.

### EXTRA - Jacob Bourjaily (NBIA)

7 November 2017

Å73121 - 13.45

Title: The Surprising Simplicity of Scattering Amplitudes.

Abstract: The way that we understand, teach, and use quantum field theory to make predictions for experiments is rapidly changing in order to make the *simplicity* of our predictions less surprising (and hence also easier to compute). Indeed, whether for theoretical exploration or practical applications, the methods described in textbooks are no longer those being used by experts today. In this talk, I will describe some of our recent advances that have been made to explain this simplicity and how they have been used to dramatically extend predictive reach. Much of this progress has so far been made for especially simple quantum field theories, but many of the lessons learned have much wider applicability. I will describe the status of these generalizations today, and the concrete roads ahead.

### Sebastian Franco (CUNY)

1 November 2017

Å73121 - 13.45

Title: Going Beyond Duality Using Branes.

Abstract: Engineering quantum field theories in String Theory in terms of branes is a powerful approach for understanding their dynamics. I will first present recent progress in the realization of 2d N=(0,2) gauge theories in terms of branes. I will discuss Brane Brick Models, a novel class of Type IIA brane configurations, which are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the infinite class of 2d (0,2) quiver gauge theories on the worldvolume of the D1-branes and substantially streamline their connection to the probed geometries. In a second part, I will explain how mirror symmetry provides a geometric unification of order n gauge theory dualities in different dimensions.

### EXTRA - Andreas Gustafsson (KIAS)

26 October 2017

Å73121 - 15.00

Title: Five-dimensional fermionic Chern-Simons theory.

Abstract: We study 5d fermionic CS theory with a fermionic 2-form gauge potential. This theory can be obtained from 5d MSYM theory by performing the maximal topological twist. We put the theory on a five-manifold and compute the partition function. We find that it is a topological quantity, which involves the Ray-Singer torsion of the five-manifold. For abelian gauge group we consider the uplift to the 6d theory and find a mismatch between the 5d partition function and the 6d index, due to the nontrivial dimensional reduction of a selfdual two-form gauge field on a circle. We also discuss an application of the 5d theory to generalized knots made of 2d sheets embedded in 5d.

### Anton Nedelin (Milano Bicocca)

25 October 2017

Å73121 - 13.45

Title: T[U(N)] duality web: mirror symmetry and gauge/CFT correspondence.

Abstract: In this talk I will review recently obtained correspondence between partition functions of 2d GLSM and certain correlators of Toda CFT. To illustrate this correspondence I will consider particular example: the partition function of 3d T[U(N)] theory. I will start by reviewing mirror self-duality of this class of theory and will briefly derive correspondence between its holomorphic blocks and Dotsenko-Fateev representation of the correlators in q-deformed Toda CFT. Finally I will show how upon the circle reduction 3d mirror symmetry reduces to correspondence between the partition function of certain 2d N=(2,2) quiver theory and Toda CFT correlators.

### Yunfeng Jiang (ETH)

18 October 2017

Å73121 - 13.45

Title: Algebraic geometry and Bethe ansatz.

Abstract: In this talk, I will discuss how to apply methods of modern computational algebraic geometry to Bethe ansatz. I will show that algebraic geometry provides natural mathematical languages and powerful tools to understand the structure of solutions of Bethe ansatz equations (BAE). In particular, I will present new methods to count the number of physical solutions with fixed quantum numbers based on Gr\"obner basis and quotient ring. This method can be applied to study the completeness of Bethe ansatz. I will also discuss an analytical method to compute the sum of on-shell physical quantities over all physical solutions without explicitly solving BAE. This method has important applications in calculating the sum rules of OPE coefficients in N=4 super-Yang-Mills theory.

### Ingmar Saberi (Heidelberg)

11 October 2017

Å73121 - 13.45

Title: Brane quantization and the double affine Hecke algebra.

Abstract: Double affine Hecke algebras, first introduced by Ivan Cherednik, are a family of algebras labeled by a choice of root system. Cherednik used their representation theory to give a uniform proof of the Macdonald constant-term conjectures; thereafter, they have been a source of interest in mathematics and also physics, especially after they were used to construct homological invariants of torus knots by Gorsky, Oblomkov, Rasmussen, and Shende. I'll discuss some new calculations that recover aspects of DAHA representation theory from the study of a particular Hitchin moduli space, in the framework of the brane quantization program of Gukov and Witten. In the associated physical picture, the so-called "spherical" DAHA appears as an algebra of line operators in four-dimensional N = 2* theory. This is ongoing work, to appear soon with Sergei Gukov, Peter Koroteev, and Satoshi Nawata.

### EXTRA - Timothy Adamo (Imperial C.)

10 October 2017

Å73121 - 13.45

Title: Worldsheet methods for interactions on curved backgrounds.

Abstract: The study of string theory on curved background fields is notoriously difficult: quantum consistency of the worldsheet CFT imposes an infinite tower of constraints on the background fields, and calculations which were straightforward for flat backgrounds (e.g., writing vertex operators, computing 3-point functions) are practically impossible. I will discuss how certain chiral, constrained worldsheet theories (known as 'ambitwistor strings') describe QFT degrees of freedom directly and avoid many of the difficulties associated with ordinary strings on curved backgrounds. This provides a new tool for studying perturbation theory on curved backgrounds from a worldsheet perspective. As an example, we will consider certain plane wave backgrounds, and see that the worldsheet theory can be quantized, vertex operators written down, and 3-point functions computed explicitly.

### Pedro Liendo (DESY)

4 October 2017

Å73121 - 13.45

Title: Bootstrapping N=4 SYM with defects.

Abstract: We study the constraints of superconformal symmetry on 4d N=4 theories in the presence of a defect from the point of view of the bootstrap. The superconformal algebra implies that the bootstrap equations have an exact truncation which is tractable analytically. Due to a surprising connection between superconformal blocks, these results apply both to conformal interfaces and to line defects. Moreover, the truncated equations are polynomial and in general solvable, which allows to extract analytic non-perturbative resuls for the CFT data.

### Matt von Hippel (Copenhagen)

27 September 2017

Å73121 - 13.45

Title: Up to Six Loops, with help from Steinmann.

Abstract: As observed by Steinmann in the early 60's, functions appearing in scattering amplitudes not only have physical branch cuts, but also obey conditions on their double discontinuities, known as Steinmann relations. We have found these Steinmann relations to be particularly powerful in the context of the six-particle amplitude in planar N=4 super Yang-Mills. There, my collaborators and I build ansatze of "Steinmann Hexagon Functions" and then constrain them using a small list of physical conditions. We also obtain additional constraints based on Cosmic Galois Theory, a mathematical conjecture that constrains the constants which appear in scattering amplitudes. Using these methods we compute the complete amplitude through six loops with no need to draw Feynman diagrams or perform Feynman integrals.

### Johan Henriksson (Oxford)

13 September 2017

Å73121 - 13.45

Title: High Spin Bootstrap of Conformal Gauge Theories.

Abstract: The analytic conformal bootstrap offers new possibilities of studying conformal field theories using the crossing equation and consistency conditions. We present the recent method of using twist conformal blocks to study the high spin asymptotics of CFT data. We apply the method to weakly coupled gauge theories and derive the most general form of the one-loop four-point correlator without referring to the usual Feynman approach. It enables us to recover known correlators from the N = 4 super Yang-Mills theory.

### -------------------------------------------------------------

### 2016/2017

### Dongwook Ghim (Seoul Nat'l University)

21 June 2017

Å73121 - 13.45

Title: Elliptic Genera of 2d (0, 2) gauge theories from Brane Brick Models.

Abstract: I will present recent developments in understanding the dynamics of 2d (0,2) supersymmetric gauge theories, in particular obtained by a novel brane construction, called brane brick. Those theories are world-volume theories of D1 brane which transverse geometry is given by non-compact toric Calabi-Yau 4-cone. Briefly reviewing their construction and nice interplay between physics and geometry around them, I will introduce the recent progress in quantitative study of them with elliptic genus, an elliptic analog of Witten index. Recent findings suggest that non-linear sigma model (NLSM), which target space is a toric CY4 we probe, arises at the IR fixed point of RG flow triggered at 2d (0,2) gauge theories from brane brick. Several subtle but important issues, like gauge anomaly, in defining and computing the elliptic genus would be also discussed.

### Sergio Benvenuti (SISSA)

16 June 2017

Å73121 - 13.45

Title: Abelianization and Sequential Confinement in 2 + 1 dimensions.

Abstract: We consider the lagrangian description of Argyres-Douglas theories of type A2N−1, which is a SU(N) gauge theory with an adjoint and one fundamental flavor. An appropriate reformulation allows us to map the moduli space of vacua across the duality, and to dimensionally reduce. Going down to three dimensions, we find that the adjoint SQCD “abelianizes”: in the infrared it is equivalent to a N = 4 linear quiver theory. Moreover, we study the mirror dual: using a monopole duality to ”sequentially confine” quivers tails with balanced nodes, we show that the mirror RG flow lands on N = 4 SQED with N flavors. These results provide a physical derivation of previous proposals for the three dimensional mirror of AD theories. A crucial ingredient in our analysis is a concept of chiral ring stability, that dynamically removes some superpotential terms.

### Marcus Berg (Karlstads)

15 June 2017

Å73121 - 11.15

Title: Hybrid String Amplitudes and RNS.

Abstract: The RNS/pure spinor hybrid formalism for computing string amplitudes can keep less-than-maximal supersymmetry manifest. It also provides a natural description of backgrounds sourced by RR fields, like Anti-de Sitter space. I will give a brief introduction and sketch a few tree-level and one-loop string amplitude calculations, some old and some work in progress, e.g. recreating flat-space results from arXiv:1603.05262.

### Alexios Polychronakos (CUNY)

13 June 2017

Å73121 - 13.45

Title: Duality, Solitons and Hydrodynamics in Generalized Calogero Models.

Abstract: TBA.

### Peter Koroteev (UC Davis)

07 June 2017

Å73121 - 13.45

Title: BPS/CFT and Large-N Gauge Theories.

Abstract: We shall revisit the BPS/CFT correspondence (AGT in particular) in the context of recent progress in mathematical literature. It was found that representations of some algebras (i.e. double affine Hecke algebra) or rank N have interesting stable limits when N becomes large. These observations have both physical and mathematical significance, in particular one may formulate the BPS/CFT correspondence in this way. I shall review recent results and work in progress on these matters.

### Francesco Sala (IPMU)

02 June 2017

Å73121 - 13.45

Title: From instanton counting to Cohomological Hall algebras.

Abstract: Cohomological Hall algebras associated with preprojective algebras of quivers play a preeminent role in geometric representation theory and mathematical physics. For example, if the preprojective algebra is the one of the Jordan quiver (i.e., the quiver with one vertex and one loop), the corresponding CoHA contains the Maulik-Okounkov Yangian associated with the Jordan quiver. It acts on the equivariant cohomology of Hilbert schemes of points on the complex affine plane ("extending" the previous results of Nakajima, Grojnowski, Vasserot, etc for actions of Heisenberg algebras) and of moduli spaces of framed sheaves on the complex projective plane. The latter action yields an action of W-algebras and hence provides a proof of the Alday-Gaiotto-Tachikawa conjecture for pure supersymmetric gauge theories on the real four-dimensional space. In the present talk, I will introduce and describe CoHAs associated with the stack of Higgs sheaves on a smooth projective curve. Moreover, I will address the connections with representation theory and gauge theory.

### Amihay Hanany (Imperial College)

31 May 2017

Å73121 - 13.45

Title: Five Dimensional Gauge Theories and Higgs branch at Infinite Coupling.

Abstract: A long standing problem is to figure out the Higgs branch of a 5d supersymmetric gauge theory when all parameters are set to zero. Such theories are generically constructed with branes by a web of five branes in Type IIB superstring theory. The problem is solved in an elegant way by presenting a 3d N=4 quiver theory, invoking an interesting 5d-3d correspondence. The Coulomb branch of the 3d gauge theory is the Higgs branch at infinite coupling of the 5d gauge theory, both being HyperKahler cones. Many features of the 5d theory including mesons, baryons and relatively new objects called instanton operators are captured by monopole operators, casimir invariants, and dressed monopole operators of the 3d theory.

### Gabriele Ferretti (Chalmers)

24 May 2017

Å73121 - 13.45

Title: Gauge theories of partial compositeness.

Abstract: We present a class of gauge theories in which the Higgs boson arises as a pseudo-Nambu-Goldstone boson (pNGB) and top-partners arise as bound states of three hyperfermions. A common feature they all share is the presence of specific additional scalar resonances, namely two neutral singlets and a colored octet, described by a simple effective Lagrangian. We study the phenomenology of these scalars and develop a generic framework which can be used to constrain them.

### Piotr Surowka (Harvard)

17 May 2017

Å73121 - 13.45

Title: Topology, supersymmetry and hydrodynamics.

Abstract: Fluid mechanics can be formulated in terms of effective actions. However, different quantum field theories can lead to different fluids. Microscopic details are encapsulated in the hydrodynamic gradient expansion and a set of transport coefficients that include, for example, viscosity or coefficients due to quantum anomalies. First I will explain how effective actions can be constructed for non-dissipative fluids. Next I will show how to include dissipation which leads to supersymmetric degrees of freedom. I will explicitly analyze the Langevin dynamics, the simplest model that illustrates a construction of the effective action for a dissipative system.

### Johanna Knapp (Vienna)

15 May 2017

Å73121 - 13.45

Title: Gauged Linear Sigma Model, Calabi-Yaus and Hemisphere Partition Function.

Abstract: The gauged linear sigma model (GLSM) is a supersymmetric gauge

theory in two dimensions which captures information about Calabi-Yaus and

their moduli spaces. Recent result in supersymmetric localization provide

new tools for computing quantum corrections in string compactifications.

This talk will focus in particular on the hemisphere partition function in

the GLSM which computes the quantum corrected central charge of B-type

D-branes. Several concrete examples of GLSMs and the application of the

hemisphere partition function in the context of transporting D-branes in

the Kahler moduli space will be given.

### Sergey Alexandrov (Montpellier)

10 May 2017

Å73121 - 13.45

Title: D-instantons, mock modular forms and BPS partition functions.

Abstract: I'll discuss the modular properties of D3-brane instantons

appearing in Calabi-Yau string compactifications. I'll show that

the D3-instanton contribution to a certain geometric potential on

the hypermultiplet moduli space can be related to the elliptic

genus of (0,4) SCFT. The modular properties of the potential imply

that the elliptic genus associated with non-primitive divisors

of Calabi-Yau is only mock modular. I'll show how to construct

its modular completion and to make manifest the modular invariance

of the twistorial construction of D-instanton corrected hypermultiplet

moduli space.

### Juan Pedraza (Amsterdam)

3 May 2017

Å73121 - 13.45

Title: Linear response of entanglement entropy from holography.

Abstract: In this talk I will present recent results of the propagation of entanglement entropy after a global quench in the context of AdS/CFT. I will start by reviewing the heuristic picture for the entanglement propagation after instantaneous quenches dubbed as 'entanglement tsunami', and explain why this interpretation fails for general quenches and entangling regions. In the second part of the talk I will present an analytic perturbative calculation for small subregions and show that in this regime the spread of entanglement exhibit some distinct features, most notably, that the instantaneous rate of growth is not constrained by causality, but rather its time average. Finally, I will argue that for small subregions, the growth of entanglement after general global quenches can be physically understood in terms of a linear response theory.

### Vishnu Jejjala (Johannesburg)

26 April 2017

Å3419 - 13.45

Title: Hot Attractors.

Abstract: Non-extremal black holes, which emit thermal Hawking radiation, have two horizons: the event horizon or outer horizon and the Cauchy horizon or inner horizon. Surprisingly, for a broad class of solutions to the Einstein equations, the product of the areas of the inner and outer horizons is the square of the area of the horizon of the zero temperature black hole obtained from taking the smooth extremal limit. We use the attractor mechanism in supergravity to motivate this result. Non-extremal geometries at the Reissner-Nordström point, where the scalar moduli are held fixed, can be lifted to solutions in supergravity with a near-horizon AdS3×S2. These solutions have the same entropy and temperature as the original black hole and therefore allow an interpretation of the underlying gravitational degrees of freedom in terms of CFT2. Symmetries of the moduli space enable us to explicate the origin of entropy in the extremal limit.

### Nadav Drukker (King's)

19 April 2017

Å73121 - 13.45

Title: Matrix models for the gauge-gravity correspondence.

Abstract: Localization reduces the calculation of certain observables in supersymmetric field theories to matrix models. I will review three examples of matrix models that arise in N=4 SYM and ABJM theory. In particular I will focus on how the solution of the matrix model, either the exact solution, or the large N one, leads to exact predictions for the AdS duals of these theories. In the case of the Schur index, there is still no satisfactory holographic counterpart to the gauge theory result.

### Ilmar Gaharamanov (MPI)

12 April 2017

Å73121 - 13.45

Title: Progress in integrable statistical models inspired by supersymmetric gauge theories.

Abstract: Recently, there has been observed several connections of integrable models to supersymmetric gauge theories and special functions of hypergeometric type. One of such connections is a correspondence between supersymmetric quiver gauge theories and integrable lattice models such that the integrability emerges as a manifestation of supersymmetric dualities. Particularly, partition functions of supersymmetric quiver gauge theories with four supercharge on different manifolds can be identified with partition functions of two-dimensional exactly solvable statistical models. This relationship has led to the construction of new exactly solvable models of statistical mechanics, namely the Yang-Baxter equation was solved in terms of new special functions. In the talk, I will present some new solutions of the Yang-Baxter equation and related basic and hyperbolic hypergeometric integral identities.

### Fabio Riccioni (La Sapienza University)

05 April 2017

Å73121 - 13.45

Title: On orientifold truncations and spacefilling branes.

Abstract: We consider in any dimension the supersymmetric Z_2 truncations of the maximal supergravity theories. These include all orientifold truncations together with additional truncations that can be formally interpreted as being generated by non-perturbative duals of the orientifold planes. In each dimension and for each truncation we determine all the sets of space-filling branes that preserve the supersymmetry of the truncated theory. We show that in any dimension below eight these sets always contain exotic branes, that are objects that do not have a ten-dimensional origin. We finally repeat the same analysis for half-maximal theories and for the N=2 theory in four dimensions.

### David Marsh (Cambridge)

29 March 2017

Å73121 - 13.45

Title: Many-field inflation.

Abstract: nflation provides a remarkably simple explanation of the origin of structure in the universe. However, the micro-physics governing inflation is poorly known, and even some of the most basic questions like “What degrees of freedom were dynamically important in the early universe?” remains unanswered. Present cosmological observations are consistent with single-field models of inflation, but, as I will review, multi-field models are both theoretically well-motivated and phenomenologically rich. Unfortunately, they are also hard to study. This has confined the vast majority of previous studies to the two-field case, while the general case of *N ≫1* interacting fields has remained intractable. In this talk, I will present a new method for studying models of many-field inflation using non-equilibrium random matrix theory, and I will discuss the generation of observables during inflation in these models. Strikingly, as the number of interacting fields (and hence the complexity of the model) increases, the power spectra of curvature perturbations simplify, and become more predictive. These simplifications can be attributed to eigenvalue repulsion in the Hessian matrix, which can be expected to extend to a much broader class of models than those studied here. I will present explicit results for *N=100* fields, and briefly discuss observational targets for the next generation of cosmological experiments.

### Lorenzo Bianchi (DESY)

22 March 2017

Å73121 - 13.45

Title: Conformal defects: from entanglement to emitted radiation.

Abstract: In this talk, after introducing conformal defects and describing some of their interesting features, I will apply this general framework to two apparently unrelated fields. First I will discuss Rényi entropies in conformal field theories and then the Bremsstrahlung function for integrable superconformal field theories (in particular N=4 SYM and ABJM). In conclusion, I will point out some interesting relations and connections between these two examples.

### Can Kozcaz (Harvard)

15 March 2017

Å73121 - 13.45

Title: Cheshire Cat Resurgence and Self-Resurgence.

Abstract: We explore a one parameter ζ-deformation of the quantum-mechanical Sine-Gordon and Double-Well potentials which we call the Double Sine-Gordon (DSG) and the Tilted Double Well (TDW), respectively. In these systems, for positive integer values of ζ, the lowest ζ states turn out to be exactly solvable for DSG – a feature known as Quasi-Exact-Solvability (QES) – and solvable to all orders in perturbation theory for TDW. For DSG such states do not show any instanton-like dependence on the coupling constant, although the action has real saddles. On the other hand, although it has no real saddles, the TDW admits all-orders perturbative states that are not normalizable, and hence, requires a non-perturbative energy shift. Both of these puzzles are solved by including complex saddles. We also show that the perturbative series is self-resurgent, a one-to-one relation between the early terms of the perturbative expansion and the late terms of the same expansion.

### Alexandros Anastasiou (Nordita)

08 March 2017

Å73121 - 13.45

Title: Yang-Mills origin of gravitational symmetries.

Abstract: A recurring theme in the attempts of understanding the quantum theory of gravity is the idea of “gravity as the square of Yang-Mills”. This involves the tensoring of the multiplet content of two super-Yang-Mills theories to obtain the multiplet content of a supergravity theory. A complete understanding of this correspondence requires studying how the gravitational symmetries originate from the corresponding Yang-Mills factors. In this talk I will show how both the global and local symmetries of linear supergravity arise from the corresponding super-Yang-Mills ones through a dictionary between both fields and transformation parameters. Finally, I will comment on how the dictionary seems to restrict the study of dynamics to particular gauge choices.

### Yang-Hui He (Oxford)

01 March 2017

Å73121 - 13.45

Title: Gauge Theories: Quivers, Dessins and Calabi-Yau.

Abstract: We discuss how bipartite graphs on Riemann surfaces capture a wealth of information about the physics and the mathematics of large classes of gauge theories, especially those arising from string theory in the context of AdS/CFT.

The dialogue between the physics, the underlying algebraic geometry of Calabi-Yau varieties, the combinatorics of dimers and toric varieties, as well as the number theory of dessin d'enfants becomes particularly intricate and fruitful under this light.

### Daisuke Yokoyama (King's)

22 February 2017

Å73121 - 13.45

Title: Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds.

Abstract: I am going to talk about how to derive an exact partition function of supersymmetric field theories on a supersymmetry-preserving quotient of Euclidean AdS_3 by localization. We utilized three-methods to compute 1-loop contributions because the situation in non-compact space is quite different from the one in compact space, and we wanted to make ourselves be confident about the result. I will explain at least one method out of three depending on time, and discuss the features of the partition function we derived.

### Nicolò Petri (Milano Statale)

15 February 2017

Å73121 - 13.45

Title: TBA

Abstract: TBA

### Diego Rodriguez-Gomez (Oviedo)

08 February 2017

Å73121 - 13.45

Title: Correlation functions in 4d N=2 theories.

Abstract: Correlation functions are central objects in QFT. Owing to very recent results using localization, correlators for Chiral Primary Operators (CPO’s) in 4d N=2 CFT’s can be exactly computed. In this talk we will be interested on correlators for CPO’s in large N theories, focusing in particular on N=4 SYM as well as on necklace quivers arising from its orbifolding (which, in a corner of parameter space, reduce to superconformal QCD). In the N=4 SYM case we will recover the well-known non-renormalization theorem. In the case of necklace quivers, at the perturbative orbifold point, we find that untwisted sector operators follow the same behavior as N=4, while for twisted sector operators we find striking cancellations. We also compute correlation functions between CPO’s and Wilson lines, finding, in a completely different manner, striking agreement with the conjectured matrix model of Giombi & Pestun. As a by-product of our computations, we find a factorized structure of the final result for the large-N partition function.

### Lotte Hollands (Heriot-Watt)

01 February 2017

Å73121 - 13.45

Title: BPS states, spectral networks and non-Langrangian QFT's.

Abstract: BPS states in four-dimensional quantum field theories have a geometric interpretation in terms of so-called spectral networks on two-dimensional (punctured) Riemann surfaces. In this talk I will explain that the relevant spectral networks for non-Lagrangian theories can be generated from generalized Strebel differentials. I will describe how one can count the BPS states as special Lagrangian discs ending on the spectral network, and make this very concrete in one particularly interesting example, the E6 Minahan-Nemeschansky theory. Some rather beautiful pictures come up!

### Shamil Shakirov (Harvard)

25 January 2017

Å73121 - 13.45

Title: Refined Chern-Simons theory at genus 0,1,2.

Abstract: TBA

### Antonio Pittelli (Surrey)

18 January 2017

Å73121 - 13.45

Title: Dualities and Integrability in Low Dimensional AdS/CFT.

Abstract: Dual superconformal symmetry (DSC) underlies the duality between scattering amplitudes and Wilson loops in N=4 super Yang-Mills theory. Via AdS/CFT, this corresponds to the invariance of the AdS_5 x S^5 superstring action under specific T-dualities. Furthermore, DSC and T-self-duality are deeply connected with the integrability and the Yangian symmetry of the model. We show that this symmetry holds also for AdS_2 x M^8 and AdS_3 x M^7 superstrings with exceptional isometry supergroups, which imply the DSC of their still mysterious CFT duals. We then focus on AdS_2 x S^2 x T^6 superstrings and discuss their peculiar worldsheet S-matrix, as well as the infinite dimensional symmetry behind the model: the Y[gl_c(1|1)] Yangian.

### Alessandro Pini (Oviedo)

14 December 2016

Å73121 - 13.45

Title: Hilbert Series and aspects of the moduli space of instantons on CP^2.

Abstract: In the first part of the talk I give an introduction to the computational tool called "Hilbert Series" (HS). I analyze how it can be employed for the characterization of the moduli space of vacua of a QFT and of the moduli space of instantons. Then, in the second part of the talk, I discuss the moduli space of (framed) self-dual instantons on CP^2. These are described by an ADHM-like construction which allows to compute the Hilbert Series of the moduli space. The latter has been found to be blind to certain compact directions. I probe these directions, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings. Moreover I discuss the ADHM-like construction of instantons on CP^2/Z_n as well as compute its Hilbert series. As in the unorbifolded case, these turn out to coincide with those for instantons on C^2/Z_n.

### David Vegh (Utrecht)

7 December 2016

Å73121 - 13.45

Title: Segmented strings.

Abstract: Segmented strings in flat space are piecewise linear string solutions. Kinks between the segments move with the speed of light and their worldlines form a lattice on the worldsheet. This description can be generalized to anti-de Sitter spacetime where the string motion is non-linear. In this talk, I will review the properties of segmented strings and relate them to discrete-time Toda-type lattices.

### Masanori Hanada (Stanford and Kyoto)

30 November 2016

Å73121 - 13.45

Title: Black Holes and Random Matrices.

Abstract: Maldacena suggested that the late-time behavior of the correlation functions can diagnose the discrete energy spectrum of the black hole microstates. In order to determine such long-time property in the quantum field theories dual to black holes, we consider the Sachdev-Ye-Kitaev (SYK) model as an ideal toy model. We study the correlation functions and the spectral form factor, which is essentially the analytic continuation of the thermal partition function to the Minkowski time, and numerically demonstrate that the long-time behavior of the spectral form factor of the SYK model is reproduced by the Random Matrix Theory (RMT). We argue that super Yang-Mills theory would exhibit the same property, and comment on possible implications to quantum gravity.

### Costis Papageorgakis (Queen Mary)

23 November 2016

Å73121 - 13.45

Title: The Nekrasov-Shatashvili Limit of the 5D Superconformal Index.

Abstract: I will motivate and introduce the Nekrasov-Shatashvili (NS) limit of the five-dimensional N=1 superconformal index. I will then summarise recent results of Cordova and Shao, who related the so-called Schur limit of the four-dimensional N=2 index to the BPS spectrum of 4D theories on the Coulomb branch. Finally, I will describe how the technology of Cordova-Shao can also reproduce the NS index in 5D for simple examples of U(1) theories. In this picture, the 5D instanton solitons are interpreted as additional flavour nodes to an associated 5D BPS quiver.

### Cyril Closset (CERN)

16 November 2016

Å73121 - 13.45

Title: The three-dimensional A-twist and supersymmetric partition functions.

Abstract: Three-dimensional N=2 supersymmetric theories can be defined on curved spaces, such as the three-sphere, that preserve (at least) half of the supersymmetry of flat space. To a large extend, this can be understood in terms of the topological A-twist of a two-dimensional N=(2,2) supersymmetric theory obtained by compactification on a circle. In this talk, I will show how this 2d point of view allows us to compute supersymmetric partition functions of 3d N=2 gauge theories (and other correlation functions of loop operators) on any U(1) principal bundle over a Riemann surface Sigma_g. This includes in particular the round three-sphere partition function, and the so-called twisted indices on the product spaces Sigma_g*S^1. I will also discuss some applications of those results.

### Sara Pasquetti (Milano Bicocca)

09 November 2016

Å73121 - 13.45

Title: 3d N=2 dualities with monopole superpotentials.

Abstract: D3 branes stretching between webs of (p,q) 5branes provide an interesting class of 3d N=2 theories. IIB S-duality is realized as 3d mirror symmetry. In the Abelian case we use the Kapustin-Strassler piece-wise dualization to obtain the low energy description of D3 branes ending on pq-webs made of many coincident NS5's intersecting one D5. Interestingly, these theories involve monopole operators in the superpotential. We also consider generalizations to non Abelian gauge theories, leading to Aharony-Seiberg dualities with monopole superpotentials.

### Yang Zhang (ETH)

02 November 2016

Å73121 - 13.45

Title: A ZURIch-based InTEgral-determination method.

Abstract: Multiloop amplitude is very important for the study of LHC physics. Given large number of Feynman diagrams, we need to consider the reduction to a small number of master integrals. Usually this is achieved by Integration-by-parts (IBP) relations, however, IBP computation is often very heavy. In this talk, we show the recent progress of IBP reduction, based on generalized unitarity and new mathematical method: computational algebraic geometry. Our package, AZURITE, which is designed to find master integrals will be presented.

### Mathew Bullimore (Oxford)

26 October 2016

Å73121 - 13.45

Title: Vortices and Vermas.

Abstract: In 3d gauge theories, monopole operators create and destroy vortices. I will explore this idea in the context of 3d supersymmetric gauge theories in the presence of an omega background, and explain how it leads to a finite version of the AGT correspondence.

### Johan Blåbäck (Saclay)

19 October 2016

Å73121 - 13.45

Title: There and back again: A T-brane's tale.

Abstract: In some particular backgrounds the non-Abelian dynamics of a

stack of Dp-branes can be described by an Abelian polarised D(p+2)-brane

with worldvolume flux. By investigating the defining equations for

T-branes, we find a new "polarised" state for a stack of non-Abelian

Dp-branes where the "polarised" frame is a single Abelian Dp-brane where the

original T-branes data is encoded as worldvolume curvature. We will join an

explicit T-brane construction's journey through T-dualities and brane

polarisation to reach this new Abelian T-brane description.

### Seyed Morteza Hosseini (Milano Bicocca)

12 October 2016

Å73121 - 13.45

Title: The origin of AdS black hole/string microstates from topologically twisted index.

Abstract: We provide general formulae for the topologically twisted index of a general three/four-dimensional N = 2 / N = 1 quiver gauge theories in the limits for which holography becomes applicable. After reviewing the results for the ABJM theory, we move to compute the index of N = 4 SYM and N = 1 Klebanov-Witten theory, and reproduce the "entropy" of AdS_5 black strings. An extremization of the index with respect to a set of chemical potentials is required which is equivalent to the c-extremization principle. As a final bonus, our computations reveal an intriguing universal RG flow from 3d/4d to 1d/2d.

### Alessandro Sfondrini (ETH)

5 October 2016

Å73121 - 13.45

Title: Integrable bootstrap in AdS/CFT.

Abstract: I will review how symmetries and integrability techniques can be used to efficiently compute certain AdS/CFT observables exactly. For most of my talk, I will be focusing on the AdS3/CFT2 backgrounds, and more specifically on the spectrum of AdS3xS3xT4 and AdS3xS3xS3xS1 super-strings in the planar (or 't Hooft) limit. I will introduce the rich physics of these backgrounds, that are related to the D1-D5 system, to CFT2s with N=(4,4) super-conformal symmetry, and in a certain limit higher-spin theories. Interestingly, and despite considerable efforts, many features of these AdS/CFT setups remain to be understood. Leaving aside most technical details, I will introduce the "integrable bootstrap" approach on the string world-sheet, highlight some key physical features that it has revealed, and discuss how it can be used to address open questions. I will conclude by sketching how this approach can be adapted to compute more general observables, such as form factors, three-point functions and one-point functions in the presence of defects.

### Marco Chiodaroli (Uppsala)

28 September 2016

Å73121 - 13.45

Title: N=2 supergravities as double copies of gauge theories.

Abstract: This talk reports on recent progress in amplitude computations for broad

classes of N=2 Maxwell-Einstein and Yang-Mills-Einstein supergravities,

using the framework provided by color/kinematics duality and the

double-copy construction. After a review of the main theoretical tools, we discuss the extension of the double-copy construction to a particular infinite family of N=2

Maxwell-Einstein theories in four and five dimensions, the generic

Jordan family of supergravities. We show that the global symmetries of these theories can be easily gauged, giving the amplitudes of the corresponding Yang-Mills-Einstein

supergravities. We also discuss how the construction can be modified to

describe spontaneous symmetry breaking. Finally, we present an extension

of the construction that captures an even larger class of N=2

supergravities with homogeneous target spaces.

### Ali Mollabashi (IPM)

21 September 2016

Å73121 - 13.45

Title: Entanglement in the Field Space: Scalar Field.

Abstract: I will start with a brief review of how the notion of quantum entanglement is uplifted from QM to QFT. Introducing various types of entanglement in the framework of QFT, the rest of the talk will be focused on a specific type which I call "entanglement in the field space". I will introduce a family of solvable scalar models and report the result of various entanglement measures in these models. I will discuss about some features of their entanglement structure and also about their possible holographic dual.

### Gustav Mogull (Edinburgh)

7 September 2016

Å73121 - 13.45

Title: Local integrands for pure Yang-Mills theory.

Abstract: Finding compact integrand representations of amplitudes in pure Yang-Mills theory requires convenient integral bases. In this seminar I will demonstrate how the infrared divergences of some D-dimensional Feynman integrals can be regulated using special choices of numerators. These choices are inspired by the existing four-dimensional local integrand structures due to Arkani-Hamed et al, valid only in the planar limit of maximally supersymmetric N=4.