Opening

• Zoltán Bajnok (Wigner RCP)

Room: Conference room -1.75

Resurgence and renormalons in integrable field theories

• Marcos Mariño (University of Geneva)

Room: Conference room -1.75 Understanding the behavior of perturbative series in quantum field theory is an old and venerable problem. In the 1970s-1980s it was found that this behavior is closely connected to non-perturbative physics, and ’t Hooft and Parisi argued that the most important non-perturbative corrections in asymptotically free theories are due to renormalons. In contrast to instantons, renormalons do not have a semi-classical description, they are difficult to compute, and they are still poorly understood. In this talk I will show that integrable, asymptotically free field theories in two dimensions provide an excellent laboratory to study renormalons. In particular, one can obtain for the first time analytic results on their structure at finite N, which turn out to challenge the standard orthodoxy on the subject. Our results also provide exact, testable trans-series representations of physical observables, i.e. extensions of perturbative series which include exponentially small corrections, as expected from the theory of resurgence.

Yangian symmetry, fishnet integrals and geometry

• Florian Loebbert (Bethe Center Bonn)

Room: Conference room -1.75 Via the fishnet-limit of AdS/CFT, individual Feynman integrals inherit a conformal Yangian symmetry. Surprisingly, this extends to certain classes of integrals with massive propagators, which suggests that integrability extends beyond the massless regime of planar $\mathcal{N}=4$ super Yang-Mills theory. We demonstrate how to use the Yangian symmetry for bootstrapping Feynman integrals from scratch. In particular, we consider the example of fishnet integrals in two spacetime dimensions where this leads to a curious interplay between algebra and geometry.

Correlation functions of determinant operators in conformal fishnet theory

• Edoardo Vescovi (Nordita)

Room: Conference room -1.75 We consider scalar local operators of the determinant type in the conformal fishnet theory that arises as a limit of gamma-deformed $\mathcal{N}=4$ super Yang-Mills theory. We generalise a field-theory approach to expand their correlation functions to arbitrary order in the small coupling constants and apply it to the bi-scalar reduction of the model. We explicitly analyse the two-point functions of determinants, as well as of certain deformations with the insertion of scalar fields, and describe the Feynman-graph structure of three- and four-point correlators with single-trace operators. These display the topology of globe and spiral graphs, which are known to renormalise single-trace operators, but with "alternating" boundary conditions.

Form factors: from integrability to bootstrap and a new duality

• Matthias Wilhelm (Niels Bohr Institute)

Room: Conference room -1.75 In this talk, I discuss three recent developments in our understanding of form factors of local operators in planar $\mathcal{N}=4$ super-Yang-Mills theory. First, I discuss how the so-called form factor operator product expansion (FFOPE) allows us to determine form factors of the chiral part of the stress tensor supermultiplet at any value of the coupling in an expansion around the (multi)collinear limit. Second, I discuss how we can use the FFOPE data to bootstrap the corresponding three-point form factor for general kinematics up to eight-loop order via its symbol. Third, I discuss a new weak-weak duality by which the three-point form factor is related to the six-point amplitude in the same theory.

Null polygons in conformal gauge theory

• Enrico Olivucci (Perimeter Institute)

Room: Conference room -1.75 I will present recent progress about n-point correlators in planar conformal gauge theory ($\mathcal{N}=4$ SYM). I will focus on the double-scaling regime when $n$ operators ($1/2$-BPS) lie at the cusps of a polygon with light-like edges and the t’Hooft coupling goes to zero. In this limit the correlators undergo a dynamical factorization into simpler objects dubbed null-polygons that we compute at high perturbative order via the stampede light-cone method. I will explain the all-loop conjecture for the polygons as the solutions of coupled 2d Toda lattice equations. This result generalizes to $n$-point the four-point “null octagon" by A. Belitski and G. Korchemsky, and shows how the nice feature of determinants shows up also for $n>4$ points correlators providing a valuable boundary condition for an integrability-based bootstrap of higher-point correlators in general kinematics. The talk is based on joint works with Pedro Vieira 2205.04476 and 2111.12131.

One more construction for Bethe vectors

• Andrii Liashyk (King's College London)

Room: Conference room -1.75 I will talk about construction of Bethe vector based onto Ding-Frenkel isomorphism that can be applied for wide class models based on Yangians and quantum affine algebras including some non-difference R-matrices like Hubbard model.

Integrable D-branes and 1pt functions

• Konstantin Zarembo (Nordita)

Room: Conference room -1.75 Bulk D-branes describe conformal defects on the boundary, and some of them may preserve integrability of the closed string. The 1pt functions in the presence of the defect are overlaps between the boundary state representing the D-brane and the Bethe eigenstate of the spin chain (or string sigma-model). Such overlaps can be efficiently computed using integrability. I will mostly concentrate on domain wall defects in ABJM.

Crosscap states, integrability and holography

• Shota Komatsu (CERN)

Room: Conference room -1.75 Crosscap states have been studied extensively in two-dimensional conformal field theory in the past, where part of the motivations came from their connection to orientifolds in string theory. Surprisingly however, analogous studies in integrable QFTs have been lacking. In this talk, I will fill this gap by presenting a systematic study of crosscap states in integrable field theories and spin chains. First, I derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. Next I will introduce crosscap states in integrable spin chains and obtain exact determinant expressions for overlaps with energy eigenstates. These states are long-range entangled and provide interesting initial conditions for the quantum quench protocol, which are quite distinct from short-range entangled states corresponding to the boundary states. Finally, I will discuss how to realize these crosscap states in planar $\mathcal{N}=4$ SYM and use it to compute observables at finite coupling. Based on joint work(s) with Joao Caetano, Leonardo Rastelli and Paolo Soresina.

Wrapping corrections for long range spin chains

• Tamás Gombor (Eötvös Lorand University)

Room: Conference room -1.75 In this talk, I show a construction of transfer matrices for long range spin chains. These transfer matrices define a large set of conserved charges for every length of the spin chain. These charges agree with the original definition of long range spin chains for infinite length. However, this new construction works for every length, providing the definition of integrable finite size long range spin chains. The properties of these finite size Hamiltonians are similar as expected from the wrapping corrections of the planar $\mathcal{N}=4$ super Yang-Mills.

Pólya formula for Jordan blocks

• Changrim Ahn (Ewha Womans University)

Room: Conference room -1.75 We consider integrable three-state spin chain models that appear in a strongly twisted, double-scaled deformation of $\mathcal{N}=4$ Super Yang-Mills Theory. These three-parameter „eclectic" models are non-diagonalizable. Their spectrum of Jordan blocks shows surprisingly subtle yet regular patterns with regard to sizes and multiplicities. In a first approach, we derive deformed Bethe equations. They are exactly solvable, scale with non-trivial critical exponents, exhibit completeness of states, and are consistent with Pólya's enumeration theorem. However, the quantum inverse scattering method does not account for the spectrum of Jordan blocks, as all Bethe vectors collapse to some trivial states. In our second approach, we start with a simpler hypereclectic spin chain model, where all parameters are set to zero except for one. Despite its extreme simplicity, it appears to reproduce the full spectrum of the eclectic model, a phenomenon we call universality. Based on combinatorics and linear algebra considerations, we derive a generating function encoding the spectrum with the help of q-binomial coefficients. We treat the full state space, as well as its physically relevant restriction to cyclic states. The latter involves a certain q-deformation of the general Pólya enumeration theorem.

Quantum symmetries in $\mathcal{N}=2$ SCFTs

• Elli Pomoni (DESY )

Room: Conference room -1.75

Lifting integrable models and long-range spin chains

• Ana Lucia Retore (School of Mathematics - Trinity College Dublin)

Room: Conference room -1.75 The presence of integrability in a model provides us with powerful tools to solve it. It plays a role in several different areas of physics, being in particular responsible for remarkable progress in the context of AdS/CFT. To ask whether a model is integrable is therefore a very relevant question, but not always an easy one. In this talk, I will discuss two methods to construct new integrable models. The first allows to classify integrable models whose Hamiltonians have nearest-neighbor interaction, while the second can also be applied to long-range spin chains. Examples will include new integrable deformations of $AdS_2$ and $AdS_3$ S-matrices; and the Lax operator and R-matrix of the two-loop $SU(2)$ sector in $\mathcal{N}=4$ SYM. I will also show that all known range 3 integrable deformations of the 6-vertex model are generated by an R-matrix. This talk will be mostly based on arxiv:2109.00017 and arxiv:2206.08390.

The AdS Virasoro Shapiro amplitude from dispersive sum rules and integrability

• Luis Fernando Alday (University of Oxford)

Room: Conference room -1.75

Nonperturbative amplituhedron geometries

• Jaroslav Trnka (University of California, Davis)

Room: Conference room -1.75 I will discuss some new developments in the context of the Amplituhedron construction for planar $\mathcal{N}=4$ SYM scattering amplitudes. I will define a negative Amplituhedron geometry which provides an all-loop order definition for a certain IR finite quantity, related to the ratio of null polygonal Wilson loops. Then I will show that the Amplituhedron picture suggests an interesting expansion of this quantity in terms of "loops of loops", unrelated to the usual small coupling expansion. In the leading order, I will provide an exact result to all orders in the coupling, and show the relation to the cusp anomalous dimension. Finally, I will discuss a certain interesting deformation of the geometric construction, and then conclude with future directions.

Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory

• Benjamin Basso (LPENS)

Room: Conference room -1.75 I will describe a conjecture for the structure constants of single-trace operators in planar $\mathcal{N}=4$ SYM, in the case where two operators are protected. The conjecture builds on the hexagon representation for long operators, which we extend to operators of any length using “spectral data” from the TBA/QSC formalism. I will also describe evidence and tests for the conjecture at weak and strong coupling.

Non-local geometry of Bethe Algebras and monodromy bootstrap

• Dmytro Volin (Uppsala University / Nordita)

Room: Conference room -1.75 Baxter $Q$-functions encoding conserved charges of an integrable model satisfy a variety of relations that are non-local in spectral parameter and have a beautiful geometric interpretation. To fix the model we should impose analytic properties on $Q$-functions and doing so consistently with the non-local geometric relations is a stringent requirement which can be used both for classification goals and as an efficient computation tool for the spectrum. In supersymmetric models where $Q$-functions feature branching points, this requirement allows to bootstrap quantum spectral curves of AdS/CFT type.

Mirror thermodynamic Bethe ansatz for AdS$_3$/CFT$_2$

• Alessandro Sfondrini (University of Padova / IAS Princeton )

Room: Conference room -1.75 I will discuss a new proposal for the dressing factors of the AdS$_3\times$S$_3\times$T$_4$ superstring supported by Ramond-Ramond background fluxes which highlights a very non-trivial interplay between gapless and gapped excitations. I will show how its analytic properties allow to construct the mirror model and its thermodynamic Bethe ansatz equations by analytic continuation. Based on work with Sergey Frolov.

Quantum Spectral Curve for AdS$_3$/CFT$_2$: a proposal

• Andrea Cavaglià (University of Torino)

Room: Conference room -1.75 In addition to the cases involving $\mathcal{N}=4$ SYM and ABJM theory, some prominent AdS3/CFT2 dualities also appear to be integrable. I will discuss the proposal for a Quantum Spectral Curve (QSC) – the mathematical tool to describe the spectrum – in the case of string theory on AdS3xS3xT4 with Ramond-Ramond flux. Contrary to the two previously known cases, the form of the QSC for this theory was fixed with a bootstrap-like consistency approach. I will discuss the logic of this proposal, some new unexpected features of this QSC, and some first applications.

On the UV behaviour of integrable theories

• Lucia Cordova (ENS Paris)

Room: Conference room -1.75 In this talk I will analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized TTbar deformations. I will show how a turning point in the TBA, interpreted as a Hagedorn temperature, arises from theories with more resonances than bound states. I will explain the numerical method which allows us to pass the turning point and discuss some properties of the unconventional UV behaviour. I will focus on theories with k resonances and — to our knowledge — a new family of UV complete integrable theories.

Gaudin integrability and harmonic analysis of conformal partial waves

• Ilija Buric (University of Pisa)

Room: Conference room -1.75 Partial wave decompositions are a central tool in the bootstrap approach to conformal field theory. In this talk, I will discuss differential equations that the partial waves satisfy. For a general $N$-point correlation function and a choice of an OPE channel, there is an associated Gaudin model with $N$ sites whose eigenfunctions coincide with the waves. This observation is a new instance of a relation between CFTs and quantum integrable systems, with potentially interesting implications for both. Two of the first applications will be described, which both originate from the OPE of the field theory: factorisation of higher-point partial waves into lower-point ones in an OPE limit, and reductions of the Gaudin model to elliptic and spinning hyperbolic Calogero-Moser-Sutherland models.

Bootstrapping the lattice Yang-Mills theory

• Zechuan Zheng (ENS Paris)

Room: Conference room -1.75 I will speak about my recent work with Vladimir Kazakov where we study the $\text{SU}(N_c)$ lattice Yang-Mills theory in the planar limit, at dimensions $D=2,3,4$, via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with the cut-off $L$ on the maximal length of loops, and the positivity conditions on certain correlation matrices. Our algorithm is inspired by the pioneering paper of P. Anderson and M. Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in the line with our previous work on matrix bootstrap. We thus obtain the rigorous upper and lower bounds on the plaquette average at various couplings and dimensions. The results are quickly improving with the increase of cutoff $L$. For $D=4$ and $L=16$, the lower bound data appear to be close to the Monte Carlo data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the $3$-loop perturbation theory. We attempt to extract the information about the gluon condensate from this data. Our results suggest that this bootstrap approach can provide a tangible alternative to, so far uncontested, the Monte Carlo approach.

Ballistic macroscopic fluctuation theory for integrable systems

• Takato Yoshimura (University of Oxford )

Room: Conference room -1.75 The macroscopic fluctuation theory (MFT) has served as a universal tool for describing the large scale nonequilibrium physics induced by rare fluctuations. While the MFT has been applied only to many-body systems that are purely diffusive so far, the underlying idea can be extended to other transport types too. In this talk, based on the ideas of the MFT, I will introduce a new theory that describes the large scale fluctuations and correlations of many-body systems that support ballistic transport. The theory, which we call the ballistic MFT (BMFT), is then applied to study the current fluctuations as well as Euler-scale dynamical correlation functions in integrable systems. It turns out that integrability of the system greatly facilitates the application of the theory, allowing us to compute the objects of interest exactly. In particular, I will present how the BMFT enables us to evaluate the full Euler-scale dynamical correlation functions in integrable systems explicitly, including their long-range contributions, which is a novel phenomenon predicted by the theory.

The Gaudin model from 3d mixed BF theory

• Benoit Vicedo (University of York)

Room: Conference room -1.75 4d Chern-Simons theory, proposed and studied by Costello, Witten and Yamazaki, provides a gauge-theoretic origin of many integrable lattice models and a very broad family of 2d integrable field theories, including those arising as Gaudin models associated with affine Kac-Moody algebras. In this talk I will describe how 3d mixed BF theory provides a similar gauge-theoretic origin for the Gaudin model associated with a finite-dimensional Lie algebra or more generally for Hitchin's integrable system. Based on joint work arXiv:2201.07300 with J. Winstone.

Segmented strings in AdS$_3$

• David Vegh (Queen Mary University of London)

Room: Conference room -1.75 In this talk, I will describe ``segmented strings'' moving in three-dimensional anti-de Sitter spacetime. The motion of a bosonic string in this target space is classically integrable and the worldsheet theory can be discretized while preserving integrability. The corresponding embeddings are segmented strings, which generalize piecewise linear strings in flat space. I will present several examples. In order to compute the spectral curve of the string, I will introduce ``brane tilings'', which are doubly-periodic planar bipartite graphs. I will show that the motion of a closed segmented string can be embedded into the cluster transformation dynamics of a certain brane tiling. This will enable us to compute the spectral curve of the string by simply taking the determinant of the adjacency matrix of the tiling. I discuss the simplest case in some detail: the closed string formed by four connected segments. A limiting case of this configuration is the folded string whose motion is restricted to a 2d subspace. I comment on quantization and the relationship to the 't Hooft equation, which describes meson bound states in two-dimensional planar QCD.

Closing

• Didina Serban (IPhT Saclay )

Room: Conference room -1.75 Summary talk, awarding young researcher's best talk and best poster prize.