# Wednesday Seminars

The majority of seminars take place remotely these days as a consequence of the ongoing Covid-19 pandemic. There is also a nordic lecture series.

**Organizers:** Luca Cassia, Nicolo Piazzalunga

## Spring 2021

### Rob Klabbers (Nordita and Royal Inst. Tech., Stockholm)

12 May 2021, 13:45

Location: Zoom

Title: How coordinate Bethe ansatz works for Inozemtsev model

Abstract: Three decades ago, Inozemtsev discovered an isotropic long-range spin chain with elliptic pair potential that interpolates between the Heisenberg and Haldane–Shastry spin chains while admitting an exact solution throughout, based on a connection with the elliptic quantum Calogero–Sutherland model. Though Inozemtsev’s spin chain is widely believed to be quantum integrable, the underlying algebraic reason for its exact solvability is not yet well understood. As a step in this direction in arxiv:2009.14513 we introduced a refinement of Inozemtsev’s ‘extended coordinate Bethe ansatz’ and clarify various aspects of the model’s exact spectrum and its limits. I will discuss this refinement and show how it improves our control over the model. For example, in the new coordinates, the energy becomes close to additive. Moreover, both the Bethe-ansatz equations and the energy become elliptic functions, allowing for a lifting of the spectral problem to the elliptic curve, effectively rationalising it as one might expect for an isotropic spin chain. Direct comparison with the limiting models is now also possible: I will showcase the relation with the regular Bethe ansatz for the XXX chain and the Haldane-Shastry spectrum. In particular, I will show that the Inozemtsev model links the scattering states of the Heisenberg model to the Yangian highest-weight states of Haldane Shastry, while Heisenberg bound states become affine descendants in the Haldane-Shastry spectrum.

### Matthew Buican (Queen Mary, U. of London)

27 April 2021, 14:15

Location: Zoom

Title: aXb=c in 2+1D TQFT

Abstract: I will start by giving a gentle introduction to 2+1D topological quantum field theory (TQFT), the fusion of line operators in these theories, and how 1-form symmetry arises. I will then discuss recent work in which we study fusions that are, in a sense I will explain, generalizations of 1-form symmetry and reveal much about global properties of TQFT. I will illustrate the discussion with various examples from 2+1D discrete gauge theories to Chern-Simons theories with continuous gauge groups and mention various open problems.

### Yasunori Lee (Tokyo U., IPMU)

06 April 2021, 14:15

Title: Some comments on 6d global gauge anomalies

Abstract: Given a G gauge theory, there can be global (non-perturbative) gauge transformations under which the partition function is not invariant. In 6d, relevant cases include G = SU(2), SU(3), and G2, and the old computations utilizing homotopy groups affirmed that the anomalous phases can indeed arise in all three cases. On the other hand, from the modern point of view utilizing bordism groups, there should not be such global gauge anomalies in the first place. In this talk, I will describe how this apparent conflict is resolved by carefully examining the cancellation of perturbative gauge anomalies via 6d Green-Schwarz mechanism.

### Simone Giacomelli (Oxford U.)

03 March 2021, 13:45

Location: Zoom

Title: Superconformal theories from S-fold geometries

Abstract: The term S-folds denotes F-theory compactifications which involve non-trivial S-duality transformations. In this talk I will discuss 4d N=2 preserving S-folds and the worldvolume theories on D3-branes probing them. They consist of two new infinite series of superconformal theories whose distinction lies in the discrete torsion carried by the S-fold and in the difference in the asymptotic holonomy of the gauge bundle on the 7-brane. These models are connected by an interesting web of RG flows and their Higgs branches provide new examples of instanton moduli spaces.

### Yegor Zenkevich (SISSA)

03 February 2021, 13:45

Location: Zoom

Title: Networks of branes and intertwining operators

Abstract: BPS particles in supersymmetric theories form a subspace of the Hilbert space. Moreover, when one scatters a pair of BPS particles there is an amplitude for getting a new BPS particle. This endows the space of BPS particles with the structure of an algebra, while extended objects (e.g. branes) to which the particles can bound should furnish a representation of this algebra. Brane junctions in this picture become intertwining operators between representations of the BPS algebra.

I will argue that BPS states of (p,q)-strings of Type IIB string theory in a certain Omega-background form Ding–Iohara–Miki algebra, and that three- and fivebranes indeed correspond to representations of this algebra. I will introduce some brane junctions and show how they are related to 3d gauge theories living in the worldvolume of D3 branes ending on 5-branes.

Based on 1812.11961, 1912.13372, 2012.15563

## Fall 2020

### Eric Perlmutter (Caltech)

15 December 2020, 14:15

Location: Zoom

Title: Discreteness and Integrality in Conformal Field Theory

Abstract: Familiar observables in compact CFTs, such as the partition function, are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but there is poor understanding of the abstract implications of discreteness and integrality for the space of CFTs. We study these constraints in 2D CFTs and demonstrate their power to produce rigorous bootstrap-type results *without* the need for positivity. For curious reasons which we explain, CFTs with marginal operators admit special bounds. We also derive surprising results on questions of spectral determinacy -- that is, whether certain parts of the spectrum are uniquely fixed by their complement -- in non-holomorphic CFT, which go against conventional folklore. Our conclusions follow from two new mathematical results: one on holomorphic vector-valued modular forms, and the other on non-holomorphic cusp forms. The obligation to discuss 3D gravity is fulfilled. Based on 2008.02190.

### Lorenzo Bianchi

02 December 2020, 13:45

Location: Zoom

Title: Line defect correlators

Abstract: After introducing the general framework of the defect conformal bootstrap, I will consider correlation functions of local operators in the presence of a line defect in superconformal theories. I will discuss correlators of the displacement operator using localization, holography and the conformal bootstrap.

### Zohar Komargodski (Simons Center)

24 November 2020, 16:00

Title: Non-Symmetries, Confinement and Naturalness

### Jacopo Sisti (Southampton U.)

18 November 2020, 13:45

Location: Zoom

Title: Entanglement Entropy and Central Charges of 2d Boundaries and Defects

Abstract: In this talk, we discuss some results regarding the entanglement entropy and the defect central charges of two-dimensional boundaries and defects. First, we consider the AdS_{4}/BCFT_{3} correspondence proposed by Takayanagi in which we study the holographic entanglement entropy of spatial regions with arbitrary shape. Analytic expressions for some smooth domains are reproduced, including the one for a disk disjoint from the boundary. When the entangling curve intersects the boundary, a logarithmic divergent contribution occurs. We find its coefficient is determined by a function that contains information about the boundary central charges. In the second part, we discuss half-BPS surface defects in 4d N=2 supersymmetric theories. We show how to extract the defect central charges from supersymmetric localization and the AGT correspondence. Some of our results for defect central charges agree with those obtained previously via holography, showing that the latter are not just large-N and/or strong-coupling limits, but are exact.

### Anatoly Konechny

11 November 2020, 13:45

Location: Zoom

Title: Boundary renormalisation group interfaces

Abstract: Renormalisation group (RG) interfaces were introduced by I. Brunner and D. Roggenkamp in 2007. To construct such an interface consider perturbing a UV fixed point, described by a conformal field theory (CFT), by a relevant operator on a half space. Renormalising and letting the resulting QFT flow along the RG flow we obtain a conformal interface between the UV and IR fixed point CFTs. Although enjoying a full conformal symmetry this interface carries information about the RG flow it originated from. In this talk I will discuss some generalities of RG interfaces and then will focus on a special case of the RG interface between two boundary conditions of a 2D CFT which is obtained from a boundary RG flow interpolating between two conformal boundary conditions. This interface is zero-dimensional and is thus described by a local boundary-condition changing operator. I investigate its properties in concrete models and formulate some general conjectures that can help charting phase diagrams of boundary RG flows.

### Aleix Gimenez-Grau

04 November 2020, 13:45

Location: Zoom

Title: Superconformal Boundaries in 4-epsilon Dimensions

Abstract: Motivated by possible applications to critical systems with emergent supersymmetry, we study SCFTs with supersymmetry preserving boundary conditions. Our formalism is based on the conformal bootstrap and can be applied to theories with four supercharges in any, in principle continuous, number of dimensions. As an application, we calculate the two-point function of chiral operators at one loop in the epsilon expansion, and extract an infinite amount of new CFT data. We also perform an explicit Feynman diagram calculation and find perfect agreement with the bootstrap results.

### Michele Levi (NBI)

28 October 2020, 13:45

Location: Siegbahnsalen or Zoom

Title: Field Theory for Gravity at All Scales

### Dalimil Mazac (IAS)

27 October 2020, 15:30

Title: Dispersive CFT Sum Rules

Abstract: I will motivate and discuss the notion of dispersive sum rules in conformal field theory. They are sum rules satisfied by the OPE data of a four-point function as a consequence of conformal dispersion relations. Physically, they are a detailed manifestation of causality. The sum rules automatically suppress double-twist operators and therefore are ideally suited for implementing analytic bootstrap with rigorously bounded errors. In theories with a large N and large gap, the sum rules provide a direct link between bulk effective field theory and its UV completion, thus constraining bulk EFT from UV completeness. In some cases, the sum rules give rise to extremal functionals, i.e. they are an analytic explanation for optimal bounds coming from the numerical bootstrap.

### Renann Lipinski Jusinskas (Prague, Inst. Phys.)

30 September 2020, 13:45

Location: Å10101 (Siegbahnsalen)

Title: L-infinity algebras and gauge theory

Abstract: In this talk I will present some basic concepts of L-infinity algebras using Yang-Mills theory as a guiding example. The talk should be more or less self-contained, including a quick review of the Batalin-Vilkovisky formalism. If time permits, I will go through some recent results, in particular a more formal derivation of the so-called perturbiner expansions.

## Spring 2020

### Andrea Puhm (CPHT)

23 June 2020, 14:15 PM

Location: Zoom

Title: Asymptotic symmetries and celestial CFT

Abstract: The realization that soft theorems in gauge theory and gravity are manifestations of Ward identities for asymptotic symmetries has reinvigorated recent attempts at flat space holography. One of the key milestones from applying this paradigm is that it solidifies a conjectured extension of the BMS group to include superrotations, based on a newly discovered subleading soft graviton theorem. This precipitated two parallel initiatives within the field. On the one hand, the subleading soft graviton mode is a natural stress tensor candidate for a putative dual celestial CFT with a Virasoro symmetry, which provoked reexamining scattering amplitudes in a basis that makes conformal covariance manifest. On the other hand, the correspondence between the subleading soft graviton theorem and the proposed asymptotic Virasoro superrotation symmetry does not appear to be bijective and an extension to arbitrary diffeomorphisms on the celestial sphere was suggested. In this talk I will provide a unified treatment of conformally soft Goldstone modes of spontaneously broken asymptotic symmetries which will land us at the crossroads of the two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be.

### Alessandra Gnecchi (CERN)

09 June 2020, 14:15 PM

Location: Zoom

Title: On AdS7 Stability – a perturbative and non-perturbative analysis

Abstract: The stability of non-supersymmetric vacua obtained from string theory is receiving a lot of attention due to its implications for the recent generalizations of the Weak Gravity Conjecture. Starting from the known classification of supersymmetric AdS7 vacua in massive type IIA supergravity, I will present the study of their non-supersymmetric counterparts. For a large subset of them, perturbative instabilities can be found both from a 7D Supergravity analysis as well as from the study of polarization of the D6 brane action in 10D. For the remaining, perturbative stable ones, I will show the existence of a non-perturbative decay channel mediated by an NS5 bubble nucleation.

### Alberto Zaffaroni (Milano-Bicocca)

12 May 2020, 14:15

Location: Zoom

Title: Gluing gravitational blocks for AdS black holes

Abstract: I describe an entropy functional and an attractor mechanism that apply to all known supersymmetric black holes in AdS4 x S7 and AdS5 x S5 with arbitrary rotation and arbitrary electric and magnetic charge. The construction is inspired by recent results about the microscopic counting of degrees of freedom for AdS black holes.

### Gregory Korchemsky (IPT Saclay)

05 May 2020, 14:15

Location: Zoom

Title: Exact correlation functions of heavy half-BPS operators in planar N=4 SYM

Abstract: I will report on a recent progress in computing four-point correlation functions of infinitely heavy half-BPS operators in planar N = 4 SYM. Taking advantage of integrability of the theory, it has recently been realized that these correlation functions can be constructed in terms of fundamental building blocks – the octagon form factors. We demonstrate that these functions satisfy a system of nonlinear integro-differential equations which are powerful enough to fully determine their dependence on the ’t Hooft coupling and two cross ratios. At weak coupling, solution to these equations yields a known series representation of the octagon in terms of ladder integrals. At strong coupling, we develop a systematic expansion of the octagon in the inverse powers of the coupling constant and calculate accompanying expansion coefficients analytically.

### Iñaki García-Etxebarria (Durham University)

21 April 2020, 14:15

Location: Zoom

Title: IIB flux non-commutativity and the global structure of field theories

Abstract: I will discuss the origin of the choice of global structure (or equivalently, the choice for which higher p-form symmetries are present in the theory) for various Lagrangian and non-Lagrangian field theories in terms of their realization in IIB and M-theory. I will explain how this choice on the field theory side can be traced back to the fact that fluxes in string/M-theory do not commute in the presence of torsion. I will illustrate how these ideas provide a stringy explanation for the fact that six-dimensional (2,0) and (1,0) theories generically have a partition vector (as opposed to a partition function) and explain how this reproduces the classification of N=4 theories provided by Aharony, Seiberg and Tachikawa. Time permitting, I will describe how to use these ideas to determine the global structure for the Argyres-Douglas theories, and how this can be used to test recently proposed N=1 Lagrangians for some of these theories.

### Itamar Yaakov (Milano-Bicocca)

25 March 2020

Title: Supersymmetric Rényi entropy and charged hyperbolic black holes

Location: Zoom

Abstract: I will present an AdS/CFT computation matching the entropy of supersymmetric electrically charged hyperbolic black holes in four and six dimensions. Hyperbolic black holes are a class of black holes with non-compact horizons which are especially simple to deal with. The CFT calculation is a localization calculation on the squashed/branched sphere with vortex-like defect insertions. It is related in an interesting way to the Supersymmetric Rényi entropy of the dual gauge theory.

### Michele Levi (NBI)

13 March 2020

Title: QFT in the service of gravity

Abstract: In this talk I will present state of the art in PN gravity, and its significant advancement via the EFT of gravitating spinning objects. First, I will introduce the tower of EFTs for the binary inspiral problem. I will then present the intricate formulation of the EFT of spinning objects. Finally, I will present advanced results accomplished uniquely within this framework.

### Michael Reiterer (Hebrew University)

04 March 2020

Title: A homotopy BV algebra for Yang-Mills and color-kinematics

Abstract: Standard Feynman rules for Yang-Mills tree amplitudes fail to comply with the Bern-Carrasco-Johansson/color-kinematics duality. I will make the point that this failure is due to homotopies. These homotopies are local multilinear operations that jointly define a homotopy Batalin-Vilkovisky algebra structure for Yang-Mills on Minkowski spacetime, an algebraic upgrade of standard Yang-Mills. When this homotopy BV structure is rectified, it yields Feynman rules that do comply with BCJ/color-kinematics duality. All relevant algebraic terminology will be introduced from scratch. Based on arXiv:1912.03110.

### Thorsten Schimannek (University of Vienna)

27 February 2020

Title: The quantum geometry of genus one fibered Calabi-Yau threefolds

Abstract: The enumerative geometry of Calabi-Yau manifolds and its interplay with string dualities, most notably mirror symmetry, is by now a classical topic. Nonetheless it continues to lead to new insights in mathematics as well as string theory. In particular, there has been a renewed interest in the properties of genus one fibered Calabi-Yaus, mainly due to their importance for F-theory and geometrical engineering of gauge theories. I will review the basics of topological strings and topological branes and then describe recent progress in understanding and leveraging the quantum geometry of Calabi-Yau manifolds that exhibit a genus one fibration. The results are, via dualities, related to the supersymmetry protected quantities of a variety of different physical theories. The talk is based on 1902.08215, 1910.01988, 1911.09697 and 1912.09493.

### Anton Nedelin (Technion)

19 February 2020

Title: Black holes, Bethe Ansatz and toric geometry

Abstract: Recently there has been a considerable progress in understanding microstate counting of asymptotically-AdS black holes using index computations in the dual CFTs. One of the methods that was crucial for this progress is the so called Bethe Ansatz method which was used to evaluate large-N behaviour of the superconformal index of N=4 SYM. In this talk I will briefly review this method and discuss its generalization to the large class of toric theories. I will give examples of calculations for T11 theory and infinite class of Ypq theories. Finally I will argue how our results relate large-N behaviour of the index with the toric geometry of the underlying theory.

### Karapet Mkrtchyan (Scuola Normale Superiore)

12 February 2020

Title: Some remarks related to on-shell methods for amplitudes

Abstract: I will discuss the group-theoretical approach to the amplitudes, employing spinor-helicity variables concentrating on the example of the description of massive spinning particles in four dimensions to illustrate the main concept. The generalizations to higher dimensions will be discussed briefly. This talk is based on earlier work [JHEP 1608 (2016) 040] with E. Conde and E. Joung and an ongoing work with E. Joung and M. Mojaza.

### Oscar Henriksson (Helsinki)

05 February 2020

Title: Stringy instabilities in holographic gauge theories at finite density

Abstract: Holographic duality offers a tool for studying gauge theories at finite density. It is amusing (but perhaps to be expected) that the gauge theory phase that is best understood with conventional perturbative methods has proven the most subtle to understand in holography: the color superconductor. In this talk, I will discuss a stringy instability of charged black brane solutions termed brane nucleation, wherein the system can lower its free energy by placing some of the N D-branes at a finite radius in the bulk, thus realizing a phase analogous to a color superconductor. We will see this occurring in the dual of both N=4 SYM at finite R-charge density and in the Klebanov-Witten gauge theory at finite baryon density.

### Extra: Cumrun Vafa (Harvard)

28 January 2020

Title: A String Theory Perspective on Cosmology

Abstract:

I review some of the lessons we have learned from the identification of what can be constructed in string theory (string landscape) and what cannot (string swampland) and apply it to questions of interest in cosmology. These ideas lead to strong constraints both on early cosmology as well as the present and the future of our universe.

### Kiril Hristov (INRNE Sofia)

22 January 2020

Title: Gluing gravitational blocks

Abstract:

The main purpose of the talk (based on 1909.10550) is to introduce the concept of gravitational blocks, basic building blocks used for supergravity observables. They are directly inspired by the holomorphic blocks appearing in the factorization of supersymmetric partition functions in three and four dimensions. In particular I will focus on the use of the gravitational blocks for determining the entropy function of various black holes and black strings in AdS space. The resulting gluing rules give a prediction about the dual field theoretic superconformal and twisted indices.

### Lorenzo Tancredi

17 January 2020

Title: Analytic treatment of some classes of elliptic Feynman integrals

Abstract:

In this seminar I will present a set of techniques and algorithms that can be used to compute analytically complicated Feynman integrals of elliptic type. In particular, I will show how to write the results in compact form, how to analytically continue them to the whole phase-space relevant for physical applications and how to evaluate them numerically efficiently.

### Nikita Nekrasov

8 January 2020

Title: Blow-up methods in gauge theory, BPS/CFT, and quantum/classical relations

Abstract: TBA