# 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 (luca.cassia@physics.uu.se), Nicolo Piazzalunga (nicolo.piazzalunga@physics.uu.se)

## Spring 2021

### Massimo Taronna (Naples U.)

01 June 2021, 14.15

Location: Zoom 674 0966 1179

Title: Bootstrapping Inflationary Correlators in Mellin Space

Abstract: The bootstrap philosophy has found remarkable successes in the context of Conformal Field Theories. These advances were mostly consequences of powerful non-perturbative implementations of causality and unitarity which translated into key results in the context of the dual gravitational theories in Anti de Sitter space. In this talk I will discuss recent progress towards the analogous problem in de Sitter space. Making use of a recently introduced Mellin-Barnes representation for momentum space correlators, I will discuss how to express dS exchange amplitudes in terms of AdS ones and how to employ conformal bootstrap methods like the spectral representation, Mellin Amplitudes and crossing decomposition in de Sitter space.

### Viraf Mehta (Goettingen U.)

19 May 2021, 13:45

Location: Zoom

Title: Superradiance in the String Axiverse

Abstract: This work uses state-of-the-art computational geometric tools to directly manipulate the topological information contained in the infamous Kreuzer-Skarke database to derive axion data for compactifications of Type IIB string theory, including systems at the maximal Hodge number, 491. We discuss the physics of these multiaxion models focussing, in particular, on the constraints derived from observed spinning black holes.

### 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.