Titres & Abstracts

-- Zoltan Bajnok (Budapest), "CFT 3-point functions from integrability"

In this talk I will explain how the integrable scattering description of 2D CFTs can be used to describe diagonal 3-point couplings. I will do it by expanding explicitly the massive TBA equations at small volumes and comparing them to the perturbative CFT expansions. Our results are explicitly written in terms of CFT Y-functions. We also extend the analysis for other operators using the fermonic basis.

-- Vladimir Bazhanov (Canberra) "A distant descendant of the six-vertex model"

In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local ``spin variables'' can take arbitrary integer values, i.e., the number of possible spin states at each site of the lattice is infinite. There is also an equivalent ``dual'' formulation of the model, where the spins take continuous real values on the circle. From algebraic point of view this model is closely related to the to the 6-vertex model. It is connected with the construction of an intertwiner for two infinite-dimensional representations of the quantum affine algebra $U_q(\widehat{sl}(2))$ without the highest and lowest weights. The partition function of the model in the large lattice limit is calculated by the inversion relation method. Amazingly, it coincides with the partition function of the off-critical 8-vertex free-fermion model.

-- Hermann Boos (Wuppertal), "Application of the hidden fermionic structure to the integrable QFT"

We discuss the hidden fermionic structure of the six vertex model as well as its applications to the CFT and the sine-Gordon model. The key role in the above construction is played by the transcendental function $\omega$. Our special attention will be paid to the discussion of few recent results on the properties of this function.

-- Philippe Di Francesco (Saclay and Illinois), "Arctic curves for vertex models"

Two-dimensional integrable lattice models that can be described in terms of (non-intersecting, possibly osculating) paths with suitable boundary conditions display the arctic phenomenon: the emergence of a sharp phase boundary between ordered cristalline phases (typically near the boundaries) and disordered liquid phases (away from them). We show how the so-called tangent method can be applied to models such as the 6 Vertex model or its triangular lattice variation the 20 Vertex model, to predict exact arctic curves. A number of companion combinatorial results are obtained, relating these problems to tiling problems of associated domains of the plane.

-- Volodia Fateev (Montpellier), "Duality and ''Nice'' Duality in Integrable Field Theories"

We consider two types of duality: Fermion-Boson duality, i.e. duality between charged fermions and charged bosons and ''Nice'' duality between Quantum Field Theories and sigma-models on the deformed symmetric spaces. The theories with nice duality possess other nice property: in the weak coupling regime they do not have the ultraviolet divergencies in perturbation theory. Every of these theories in the conformal limit are specified by the W-algebra which have five field representation and corresponding reflection amplitudes.These amplitudes together with scatterin amplitudes permit to identidy these theories.

-- Frank Göhmann (Wuppertal), [with Karol Kozlowski], "Space-like asymptotics of the transverse two point functions of the XXZ chain at finite temperature"

Finite temperature dynamical correlation functions of Yang-Baxter integrable quantum chains can be represented by thermal form-factor series. These are series in which every term is expressed in terms of the spectral data and the form factors of an appropriately defined dynamical quantum transfer matrix. We review the construction and exemplify its usefulness with the discussion of the leading term of the space-like asymptotic of the transverse correlation functions of the XXZ chain at finite temperature. We shall illustrate our prediction by first discussing the special case of the XX chain, and then the case of the low-T behavior of the XXZ chain at 0<\Delta<1.

-- Michio Jimbo (Kyoto), "Scientific achievements of Fedor Smirnov"

The purpose of this talk is to give a brief survey of the lifelong scientific achievements of Smirnov. Time permitting, we touch upon q-difference opers and Bethe ansatz arising from quantum toroidal algebras (joint with B.Feigin and E.Mukhin).

-- Volodia Kazakov (ENS Paris), "Spectral properties of planar CFT's in D>2: from N=4 SYM to Fishnet CFT" (pptx version)

Integrability of planar Feynman graphs in certain higher-dimensional CFT's, made possible a non-perturbative study of fundamental observables, such as the spectrum of anomalous dimensions (as functions of couplings), structure constants and correlation functions. Helped by AdS/CFT hypothesis, combined with finite gap method and quantum spin chain analogy of the perturbation theory, the spectral problem of planar N=4 SYM has been completely solved in terms of the Quantum Spectral Curve: a set of functional equations on Baxter's Q-functions. A special double scaling limit of this theory (strong gamma deformation & weak coupling) has led to the discovery of Fishnet CFT. The explicit integrability of underlying Fishnet Feynman graphs (of regular square lattice shape), noticed and described long ago by A.Zamolodchikov, sheds light on the origins of the AdS/CFT integrability. I will briefly review these achievements and present some new results: a generalization of Fishnet CFT's to any dimension and arbitrary weights of propagators as well as a peculiar Yangian symmetry of disc-shaped planar Fishnet Feynman graphs.

-- Kolya Kitanine (Dijon), "Boundary overlaps for the open spin chains"

In this talk I’ll describe a new method to compute form factors and overlaps for the spin chains in the thermodynamic limit from the Algebraic Bethe ansatz. As an illustration I’ll discuss the computation of overlaps between ground states of open spin chains after a change of one boundary magnetic field. These results can be considered as the first step to investigate the dynamics after a boundary quench.

-- Karol Kozlowski (ENS Lyon), [with Frank Göhmann], "Space-like asymptotics of the transverse two point functions of the XXZ chain at finite temperature"

-- André Leclair (Cornell), "Ultra-violet completions of TTbar perturbations of CFT"

There are in principle an infinite number of possible QFT’s that arrive to a particular CFT via the TTbar operator in the infra-red. Building on the work of Smirnov and Zamolodchikov, we show that imposing integrability strongly constrains the possibilities and we present a systematic approach to classifying such UV completions. For instance, for a Majorana spectrum description of the Ising model, there are only 2 possible UV completions, both of which have supersymmetry. For the Ising model with an E_8 spectrum appropriate to a magnetic perturbation, we provide a partial classification. Identifying the UV CFT requires subtracting the “cosmological constant”, and this led us to speculations on the actual, measured cosmological constant.

-- Sergey Lukyanov (Rutgers), "Lattice realization of Generalized Affine Gaudin Model"

The affine Gaudin model was introduced by Feigin and Frenkel in 2007 as an affine version of the original Gaudin's spin chain. Recently, for the sl(2) case, a one parameter generalization was constructed. In the talk we discuss how this Generalized Affine Gaudin Model occurs in the scaling limit of the integrable inhomogeneous XXZ higher-spin chain.

-- Giuseppe Mussardo (SISSA), "How to control the breaking of integrability"

We discuss two analytical techniques (semi-classical method and Form Factor Perturbation Theory) and one numerical method (Truncated Hilbert space Approach) to achieve the best control of non integrable quantum field theories in two dimensions.

-- Stefano Negro (NYU), "Solving the Form Factor bootstrap for Solvable Irrelevant Deformations"

In this talk I will present some recent developments in the study of the Solvable Irrelevant Deformations: the determination, in full generality, of their Form Factors. The latter are matrix elements of operators between a vacuum an an n-particle state and constitute a set of building blocks that can be used to compute correlation functions. In IQFTs, these objects satisfy a set of equations that allow us to bootstrap their exact expressions. Carrying on this procedure for Solvable Irrelevant Deformations one finds that the Form Factors take a factorised form as products of the unperturbed objects with a factor containing the effects of the perturbation. With this result, it is then possible to analyse the effect of the perturbation on correlation functions. We will see that, depending on the sign of the deformation parameters, the form factor expansion of correlation functions can be divergent or “hyper-convergent” and that these behaviours possess an intuitive interpretation in terms of particles acquiring a positive or negative size, as was recently proposed by Cardy and Doyon.

-- Kolya Reshetikhin (Tsinghua and Beijing U.), "Hybrid integrable systems"

These are quantum integrable systems which ride on the background of classical integrable systems. In this talk I will introduce the notion of such systems, and will give some examples. Also the connection with well known structures will be explained.

-- Didina Serban (Saclay), "A solvable non-unitary fermionic long range Hamiltonian with extended symmetry"

I will present a new integrable fermionic model which can be seen as a long-range extension of the XXZ model at \Delta=0. Although it is not translationally invariant, the model possesses quasi-translational symmetry. The symmetries and the spectrum are reminiscent of the Haldane-Shastry model, to which it is closely related. The model is non-unitary and has unusual properties. In the even-site case N=2L all the energies are zero and the spectrum contains Jordan blocks of size up to L+1. In the odd-site case the one-magnon spectrum is linear.

-- Samson Shatashvili (Dublin), "Diff(S1) Co-adjoint Orbits, Universal Teichmüller Space and Quantization of Conformal Welding"

I will describe the relations between the topics mentioned in the title, as well as with the two-dimensional gravity. Berezin quantization will play an important role. Based on the joint work with A. Alekseev and L. Takhtajan.

-- Leon Takhtajan, (Stony Brook) "Supersymmetry and trace formulas : Selberg trace formula"

I will explain a path integral derivation of the Selberg trace formula, which uses a new supersymmetric localization principle. The talk is based on the papers arXiv:2112.07942 and arXiv:2306.13636, joint with Changha Choi.

-- Sasha Zamolodchikov (Stony Brook) (cancelled)

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