Talk titles and abstracts

Benjamin Basso (ENS) HHL 3pt functions at strong coupling from hexagons

I will talk about structure constants of single-trace operators at strong coupling in planar N=4 SYM focussing on the heavy-heavy-light (HHL) kinematics. This is an interesting regime which permits to probe structure constants at low energy while still avoiding well-known difficulties associated with short operators in the integrability framework. In the hexagon framework only two complete mirror sums are needed to bind the hexagons around the HHL correlators, along the two edges surrounded the light protected operator. After a brief review of the formalism, I will explain how to perform these sums at strong coupling for heavy operators mapping to low-lying states above large-charge BMN vacua. The result will be shown to be in structural agreement with holographic results obtained using Witten diagrams. I will also speculate on the absence of wrapping corrections in this regime and discuss similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex in the classical limit.

Vladimir Bazhanov (Canberra) On the scaling behaviour of the alternating spin chain

In this talk I will report the results of the study of a 1D integrable alternating spin chain whose critical behaviour is governed by a CFT possessing a continuous spectrum of scaling dimensions. I will review both analytical and numerical approaches to analyzing the spectrum of low energy excitations of the model. It turns out that the computation of the density of Bethe states of the continuous theory can be reduced to the calculation of the connection coefficients for a certain class of differential equations whose monodromy properties are similar to those of the conventional confluent hypergeometric equation. The finite size corrections to the scaling are also discussed.

Olalla Castro Alvaredo (London) Entanglement Content of Quantum Particle Excitations

In this talk I will review the results of recent work in collaboration with Cecilia De Fazio, Benjamin Doyon and Istvan M. Szecsenyi. In a series of papers we have studied the entanglement of excited states consisting of a finite number of particle excitations. More precisely, we studied the difference between the entanglement entropy of such states and that of the ground state. We considered different bipartitions of the system, and a scaling limit in which both the total size of the system and of its parts are infinite, but their ratio is kept finite. We originally studied this problem in massive free 1+1 dimensional QFTs where analytic computations were possible. We have subsequently found the results to apply more widely, including to higher dimensional free theories. In all cases we find that the increment of entanglement is a simple function of the ratio between region's and system's size only. Such function, turns out to be exactly the entanglement of a qubit state where the coefficients of the state are simply associated with the probabilities of particles being localized in a particular system's region. In this talk I will describe the results in some detail and discuss their domain of applicability. I will also highlight the main QFT techniques that we have used in order to obtain them analytically and present some numerical data.

Andrea Cavagliá (King's College) Color twist fields and Separation of Variables

I will present a procedure to define a new type of single trace operators in a planar theory, by twisting the trace with a symmetry transformation. For integrable CFTs such as N=4 SYM or the fishnet model, this allows to break conformal invariance in a controllable and integrable way, corresponding to twisted boundary conditions at the level of the spectrum. I will explain why this construction is relevant for the computation of three point functions in these theories, through the method of Separation of Variables. Finally, I will present some recent insights on how the Separation of Variables works for systems with higher rank symmetries.

Frank Coronado (Perimeter) Bootstrapping the simplest correlator in N=4 SYM

I will present the full form of a four-point correlation function of large BPS operators in planar N = 4 Super Yang-Mills to any loop order. To do this I follow a bootstrap philosophy based on three simple axioms pertaining to (i) the space of functions arising at each loop order, (ii) the behaviour in the OPE in a double-trace dominated channel and (iii) the behaviour under a double null limit. I will also discuss how these bootstrap axioms are in turn strongly motivated by empirical observations up to nine loops unveiled through integrability methods.

Sergey Derkachov (St. Petersburg) Separation of variables and Basso-Dixon correlators in two-dimensional fishnet CFT

We compute explicitly the two-dimensional version of Basso-Dixon type integrals for the planar 4-point correlation functions given by conformal fishnet Feynman graphs. These diagrams are represented by a fragment of a regular square lattice of powerlike propagators, arising in the recently proposed integrable bi-scalar fishnet CFT. The formula is derived from the first principles, using the formalism of separated variables in integrable SL(2;C) spin chain.

Lorenz Eberhardt (Zürich) An exact AdS3/CFT2 duality

I will discuss string theory on AdS3xS3xT4 with pure NS-NS flux from a worldsheet point of view. I will provide evidence that the background with the lowest amount of NS-NS flux (`k=1') is dual to the large N limit of the symmetric product orbifold of T4. I will also discuss the extension of the duality to higher flux, where the dual CFT can be described in terms of a Liouville theory. Finally, I will present further checks of the duality, such as the mapping of the symmetry algebra and constraints on correlation functions.

Nikolay Gromov (King's College) QFC/CFT duality

We present the first principle derivation of the holographic dual of the planar fishnet CFT in four dimensions. The dual model becomes classical in the strongly coupled regime of the CFT and takes the form of an integrable chain of particles in five dimensions. Then we study the theory at the quantum level. By applying the canonical quantization procedure with constraints, we show that the model describes a quantum chain of particles propagating in AdS5. We prove the duality at the full quantum level in the U(1) sector and reproduce exactly the spectrum for the cases when it is known analytically.

Igor Klebanov (Princeton) Dynamics of Tensor and SYK Models

We review the combinatorics of models where the degrees of freedom are tensors of rank three. For specially chosen interactions, the Feynman graph expansion is dominated by the so-called melonic graphs in the large N limit. We present the simplest tensor quantum mechanical model for Majorana fermions, which has O(N)^3 symmetry, and compare it with the Sachdev-Ye-Kitaev model. When two tensor or SYK models are coupled by a quartic interaction, a gap can open up for sufficiently large N between two nearby lowest energy states and the rest of the spectrum. This suggests spontaneous breaking of a Z_2 symmetry. We solve the large-N Schwinger-Dyson equations and show that a symmetry-breaking operator indeed acquires an expectation values.

Shota Komatsu (IAS) Holey sheet, integrability!

I will talk about my recent work with Yunfeng Jiang and Edoardo Vescovi (and possibly about related works in progress with several others). The main subject is the three-point function of a non-BPS single-trace operator and two determinant operators in N=4 SYM, and the goal is to derive the first fully non-perturbative result for such structure constants valid even for operators of finite length, using the Thermodynamic Bethe ansatz formalism. On the worldsheet, such a correlator corresponds to an overlap between a closed string state and a boundary state describing the Giant Graviton D-brane in AdS, which can be thought of as a generalization of g-functions in 2d QFT. I first present a large N collective-field method for perturbative computations, which provides an example of Gopakumar's "open-closed-open" triality. The results obtained with this method exhibit a simple determinant structure and suggest the integrability of the boundary state. I next determine the boundary state at finite coupling using symmetry and integrability, and derive a non-perturbative expression for the ground state overlap using TBA. I then generalize it to excited states in the SL(2) sector using analytic continuation tricks and derive the determinant representations in the asymptotic limit. Finally, I point out the similarity of our result to the finite-volume one-point function in sin(h)-Gordon models obtained from the hidden Grassmann structure found by Jimbo, Miwa and Smirnov.

Igor Krichever (Columbia) The Bethe ansatz equations and integrable system of particles

In the talk a new approach for the construction of solutions of the Bethe ansatz equations of the $\widehat{\frak{sl}_N}$ XXX quantum integrable model, associated with the trivial representation of $\widehat{\frak{sl}_N}$ will be presented. It is based on interplay with the theory of coherent rational Ruijesenaars-Schneider systems. For that we develop in full generality the spectral transform for the rational Ruijesenaars-Schneider system.

Pedro Liendo (DESY) The Bootstrap Program for Defect CFT

Extended objects or "defects" are of fundamental importance in CFT, examples include boundaries, interfaces, and surface defects, and also Wilson and 't Hooft lines in gauge theories. In this talk we will give an overview of the bootstrap program applied to defect CFTs. We will present a version of crossing symmetry analogous to crossing symmetry for four-point functions in bulk CFTs, and explain how to constrain theories with it.

Dalimil Mazac (Stony Brook) Sphere packing, quantum gravity and extremal functionals

Stefano Negro (Stony Brook) A "gentle" introduction to TTbar deformed QFTs

In this talk I will introduce a particular kind of irrelevant deformation of 2D QFTs, known as $\mathsf{T}\bar{\mathsf{T}}$ deformation and review some of the results obtained recently on this subject. The general tone will be pedagogical and intended for an audience of non-experts. After defining the operator $\mathsf{T}\bar{\mathsf{T}}$ and describing its main properties, I will present some motivations which justify the interest in these peculiar deformations. I will then move on to the derivation of important non-perturbative results and describe the principal features of the deformed theories. Finally I will display some of the most recent results and a number of interesting questions that still wait for answers.

Rafael Nepomechie (Miami) Quantum groups and Bethe ansatz

The spectrum of a quantum spin chain can have degeneracies, which can be understood from the model's symmetries. We consider here the symmetries and degeneracies of anisotropic integrable open spin chains, which are associated to affine Lie algebras $\hat g$. These spin chains have quantum group symmetries corresponding to removing one node from the $\hat g$ Dynkin diagram. We also sketch the corresponding Bethe ansatz solutions. Based on work with A. Retore (arXiv 1802.04864, 1810.09048) and R. Pimenta (arXiv 1805.10144).

Enrico Olivucci (Hamburg) Dynamical Fishnet: Integrable structures and Exact Solvability

Conformal "Fishnet" theories are a rare example of a quantum conformal field theory (CFT) in higher space-time dimensions (D>2) with non-trivial interaction. Furthermore, they possess an heavy amount of Integrable quantities and features, which makes them a toy-model of unique interest and versatility for the investigation of quantum integrability in a CFT without Gauge symmetry and SUSY. The bi-scalar realization of Fishnet theory was originally obtained as a specific corner of a strong deformation of N=4 SYM. I will review the general aspects of bi-scalar theory and argue that the whole strongly-deformed N=4 SYM is itself a theory of Fishnet type ("Dynamical"). I will prove the persistence of certain Integrable structures and describe how to obtain analytic all-loop solution for many conformal data of the theory.

Raul Pereira (Dublin) The five-point function of N=4 at strong coupling

In this talk I consider the five-point function of 20' operators in type IIB supergravity. I will show how to exploit symmetries and self-consistency conditions to bootstrap the correlator both in position and Mellin space. I will highlight the new OPE data obtained and comment on generalizations of this work.

Valentina Petkova (Sofia) The octagon form factor as a determinant

Recently it has been shown by F. Coronado that the computation of a certain class of four-point functions of heavily charged and particularly polarised BPS operators in the planar N = 4 SYM theory boils down to the computation of a special form factor - the octagon. Starting from a representation for the octagon as a Fredholm pfaffian we rewrite it as a pfaffian of a semi-infinite matrix. This allows to reduce the problem to the computation of a single integral and provides an analytic expression for the octagon valid for any value of the coupling constant. At weak coupling it is given in terms of functions evaluating ladder integrals and can be furthermore reorganised as a determinant of a semi-infinite matrix with entries given by linear combinations of such functions. This confirms a conjecture of Coronado, now providing explicit analytic formula for the coefficients. This is joint work with Ivan Kostov and Didina Serban.

Leonardo Rastelli (Stony Brook)

Radu Roiban (Penn State) On the generally-relativistic 2-body problem: Orbital dynamics from double copy and effective field theory

While the flat space two-body problem is integrable, the generally-relativistic one is not starting at the next-to-leading order. In the appropriate classical limit, scattering amplitude-based techniques can yield the classical interaction of massive bodies to all orders in their velocities and to fixed order in the expansion in Newton's constant, that is a fixed order in the post-Minkowskian expansion. In this talk we review the framework of such calculations and the derivation of the third order in the post-Minkowskian expansion for the conservative Hamiltonian of a compact spinless binary system. We also describe the scattering angle at this order as well as a first comparison with numerical GR.

Paul Ryan (Dublin) Separated Variables and Factorised Wave Functions in gl(n) Spin Chains

In this talk we will review recent advancements in the SoV program for rational higher rank spin chains and demonstrate a link between SoV and Yangian representation theory. This link will then be exploited and used to determine the spectrum of the separated variables for arbitrary finite-dimensional gl(n) spin chains which will be shown to be labeled by Gelfand-Tsetlin patterns. Then, for rectangular representations, we will construct a basis that factorises the Bethe vectors into products of Slater determinants in Baxter Q-functions. This basis is constructed by repeated action of fused transfer matrices on a suitable reference state and, by construction, diagonalises the B-operator. Finally, I will construct the conjugate momenta associated to the separated variables as simple wronskian-like expressions in Q-operators.

Diego Trancanelli (Sao Paulo) Deformations of the circular Wilson loop and spectral (in)dependence

I will study deformations of the circular Wilson loop in N=4 super Yang-Mills, both at weak and strong coupling. The leading order deformation is the Bremsstrahlung function, which is computed exactly using localization, so that the focus of the talk will be on fourth and higher order deformations. I will present simple expressions for generic deformations at the quartic order at one-loop at weak coupling and at leading order at strong coupling. I will also mention a very simple algorithm (not requiring integration) to evaluate the two-loop result. Finally, I will discuss how an exact symmetry of the strong coupling sigma-model, known as spectral-parameter independence, turns out to be an approximate symmetry at weak coupling, modifying the expectation value starting only at the sextic order in the deformation.

Stijn van Tongeren (Humboldt) Integrable deformations and AdS/CFT

The integrable models that arise in the planar limit of maximally symmetric instances of AdS/CFT are periodic, and of rational type. In other words, by and large they are like the periodic XXX spin chain. Knowing of the possibility of breaking periodicity by threading a spin chain with a magnetic flux, or of e.g. the existence of the trigonometric XXZ spin chain, we can ask whether there are analogues of such models in AdS/CFT. Progress has been made on understanding this space of integrable deformations of AdS/CFT, starting on the string side by casting them as "Yang-Baxter" sigma models. I will review the construction of these models, give an overview of the types of models this gives, and discuss their interpretation in string theory and AdS/CFT, giving concrete examples and indicating open questions along the way.

Pedro Vieira (Perimeter) Octagons: Non-planar explorations in N=4

I will discuss 4pt functions of large operators in N=4 SYM and their non-planar re-summation.

Yifan Wang (Princeton) Knots from M-theory

We identify a sector of 1/8 BPS surface operators in the 6d (2,0) theory on S^1*S^5. Upon KK reduction on the S^1 factor, they correspond to 1/8 BPS Wilson loops restricted to a great S^3 in the 5d N=2 super-Yang-Mills theory on S^5. We provide strong evidence for a conjecture that such Wilson loop observables are described by an effective 3d Chern-Simons theory on this S^3 with the level analytically continued to an imaginary value. Thus the corresponding surface operators in the (2,0) theory compute topological knot invariants on S^3. In the large N limit, from AdS/CFT, these surface operators correspond to certain calibrated M2 branes in AdS_7*S^4. We compute their renormalized action and find perfect agreement with the effective CS description. Lastly we'll discuss steps towards proving this conjecture from localization.

Xi Yin (Harvard) String spectrum in RR flux background from NSR closed string field theory