Integrability, Dualities and Deformations

15 Jul 2024, 09:00 → 19 Jul 2024, 17:00 Europe/London

Computational Foundry Building (Bay Campus, Swansea University)

The conference, which will take place at Swansea University 15-19 July 2024, is focused on exploring the rapid developments in understanding deformations of integrable theories; their application to string theory sigma models; their possible AdS/CFT applications and interpretations; their connection to higher dimensional Chern-Simons theories; and their interface with the mathematics of Poisson-Lie and non-abelian dualities.

There has been significant recent progress in understanding deformations of integrable string sigma models, their relation to non-abelian and Poisson-Lie duality, and their possible AdS/CFT interpretation in terms of non-commutative field theory. These models can also be naturally recast in terms of double and exceptional field theory. Numerous interesting connections between these research areas are developing, promising to shed light on important open questions.

The goal of this conference is to bring together experts in:

• Integrable models and their deformations
• Worldsheet dualities and extended field theories
• Non-commutative and non-associative field theory
• Integrability in gauge/gravity duality

to facilitate the exchange of ideas, collaboration, and new developments across these fields.

Speakers will include:

Tim Adamo (University of Edinburgh)
Roland Bittleston (Perimeter Institute)
Marius de Leeuw (Trinity College Dublin)
Georgios Itsios (Humboldt University Berlin)
Vladimir Kazakov (ENS Paris)
Marc Magro (ENS de Lyon)
Joseph Minahan (Uppsala University)
Susanne Reffert (University of Bern)
Jun-ichi Sakamoto (INFN Turin)
Yuho Sakatani (Kyoto Prefectural University of Medicine)
David Schmidtt (Federal University of São Carlos)
Fiona Seibold (Imperial College London)
Bogdan Stefański, jr. (City, University of London)
Arkady Tseytlin (Imperial College London)
Stijn van Tongeren (Humboldt University Berlin)
Linus Wulff (Masaryk University, Brno)

Advisory Board

Olalla Castro-Alvaredo (City, University of London)
Larisa Jonke (Ruđer Bošković Institute)
Yolanda Lozano (University of Oviedo)
Konstantinos Sfetsos (University of Athens)
Arkady Tseytlin (Imperial College London)
Masahito Yamazaki (Kavli IPMU)

Organising Committee

Sibylle Driezen (ETH Zürich)
Ben Hoare (Durham University)
Tim Hollowood (Swansea University)
Dan Thompson (Swansea University)
Benoit Vicedo (University of York)

This conference continues a series of previous events:

Integrability, Dualities and Deformations 2023 in Durham
(https://indico.cern.ch/e/IDD2023)
Integrability, Dualities and Deformations 2022 in Berlin
(https://indico.cern.ch/e/IDD2022)
Integrability, Dualities and Deformations 2021 in Santiago de Compostela
(https://indico.cern.ch/e/IDD2021)
Integrability, Dualities and Deformations online seminar series 
(https://sites.google.com/view/intdualdef)

 

 

 

We acknowledge support from:

Monday 15 July

Registration

10:00 Opening

1 alpha'-corrections from O(d,d) symmetry

When the tree-level closed string effective action is reduced from D to D-d dimensions an O(d,d) symmetry appears. I will discuss how a certain necessary condition for this O(d,d) symmetry to be present can be used to determine the complete action at order alpha'^2 and all terms involving less than six fields at order alpha'^3 in the NSNS sector.

Speaker: Linus Wulff

11:00 Break

2 JT gravity & NATD

I will discuss the geometries obtained by performing super non-Abelian T-duality of the Principal Chiral Model on OSp(1|2). Inspired by what happens in the purely bosonic case the dual supergeometry is written as the supersymmetric version of AdS2 fibered over what we interpret as the superspace equivalent of the standard bosonic line. I will also discuss that in a suitable limit, the action of the three-dimensional dual model reduces to a Jackiw-Teitelboim-like (super)gravity action in two dimensions, both in the bosonic and the supersymmetric cases.

Speaker: Anayeli Ramirez

3 Principal chiral model in arbitrary magnetic field: exact solution in planar limit

The two-dimensional Principal Chiral Model (PCM) has been considered since long as an instructive example of a QFT bearing certain similarities with QCD: asymptotic freedom, dimensional transmutation with a physical mass spectrum and a non-trivial 't Hooft's large N limit. In addition, it is an integrable QFT, with the known physical S-matrix. In our 1994 paper with V.Fateev and P.Wiegmann, we found not only the exact but also explicit solution of the vacuum energy of SU(N)xSU(N) PCM in the 't Hooft limit in the presence of specific, albeit arbitrary strong, "magnetic" field (the chemical potential of density of physical particles). The shape of this field repeated the Perron-Frobenius (PF) mode on the su(N) Dynkin diagram. I will present our recent work with E.Sobko and K.Zarembo (arxiv:2312.04801) where we explicitly solved the Bethe equation for the magnetic field of arbitrary shape. We also studied this solution in the case of small deviations of the magnetic field from the PF mode and found a perfect correspondence with the known perturbative and strong coupling results. I will also mention our results of our previous work: the 1/N expansion of the energy and a possible interpretation of PCF as a 2+1-dimensional noncritical string theory, where the role of the 3rd dimension is played by Dynkin diagram.

Speaker: Vladimir Kazakov

12:40 Lunch

4 Integrability and deformations of Thirring models

In this talk, I will discuss some important aspects of integrability and deformations of the Grassmannian and Bosonic Thirring models. In the first part of the talk, I will concern with the presence of integrable defects, the generalization to coupled Thirring models, and their Backlund transformations. In the second part, I will focus on the deformations of the Thirring models, and the construction of coupled sineGordon-sineGordon models via S-duality.

Speaker: Alexis Roa Aguirre

5 Lattice discretization of 2d integrable quantum field theories from 4d Chern-Simons theory

The relationship between 2d integrable field theory and 2d integrable lattice models is discussed in the framework of 4d Chern-Simons theory. The 2d integrable field theory is realized by coupling the 4d theory to several 2d surface ordered defects, each defect is then discretized into a 1d defect. We show that the resulting 1d defects are dualized to Wilson lines, and the lattice of discretized defects realizes an integrable lattice model. Our discretization procedure works systematically for a wide class of integrable models (including trigonometric and elliptic models). This is based on a work [hep-th/2309.14412] with Meer Ashwinkumar and Masahito Yamazaki.

Speaker: Jun-ichi Sakamoto

15:00 Break

6 Dualities of Integrable Field Theories from 4d Chern-Simons Theory

In this talk, I will explore dualities of integrable field theories through the lens of four-dimensional Chern-Simons theory, where these dualities can be viewed as dualisations of order surface defects. I will begin by discussing a type of duality that emerges from the discretisation-induced dualities of surface defects. Following this, I will delve into the anomaly-inflow mechanism for surface defects, which leads us to a second form of duality. This type of duality arises from the bosonisation of free-fermion surface defects, leading us to bosonisation dualities between generalisations of the massless Thirring model and coupled Wess-Zumino-Witten (WZW) models. This talk is based on work [hep-th/2309.14412] with Jun-ichi Sakamoto and Masahito Yamazaki.

Speaker: Meer Ashwinkumar

7 Integrable defects in N=4 SYM

In this talk I will discuss the classification of integrable conformal defects in N=4 SYM theory for which the scalar fields pick up a non-trivial vacuum expectation value. Defects of this form correspond to Dirichlet boundary conditions that have a pole at the defect. These set-ups typically appear on the field theory side of probe brane set-ups in the AdS/CFT correspondence. I will discuss the properties of the different possible fuzzy spheres that can appear and present the corresponding Matrix Product States. I will also comment on the quantum field theoretic framework such as the mass matrix and propagators.

Speaker: Marius de Leeuw

Tuesday 16 July

8 Quantum supermembranes and AdS/CFT

We will review some recent work on semiclassical quantization of 11d supermembrane. We will demonstrate how quantum corrections to supermembrane partition function are consistent with AdS/CFT in the context of ABJM theory and how they represent particular higher loop terms in string loop expansion.

Speaker: Arkady Tseytlin

9 An integrable deformation of the heterotic string

A novel classically integrable model is proposed. It is a deformation of a two-dimensional principal chiral or WZW model, embedded into a heterotic σ-model. This is inspired by the bosonic part of the heterotic σ-model and its recent Hamiltonian formulation in terms of O(d,d+n)-generalised geometry. Classical integrability is shown by construction of a Lax pair and a classical r-matrix. I briefly discuss the non-trivial non-deformation limit and the deformed backgrounds as solutions of heterotic supergravity.

Speaker: David Osten

11:00 Break

10 Coordinate Bethe Ansatz for N=2 SCFTs

The study of the spectral problem of planar N=2 SCFTs and their corresponding spin chains has been an inauspicious problem. In this talk I want to present a novel approach to the coordinate Bethe Ansatz which allowed the computation of the three-magnon wave function (paper to appear) for the spin chains that capture the spectral problem of the marginally deformed Z_2 orbifold of N=4 SYM in planar limit. The novel idea is the introduction of contact terms which incorporate the dynamical structure of the spin chains and it can be generalized to n-body problem and also to more general orbifolds.

Speaker: Deniz Bozkurt

11 Scattering on effective strings and membranes

The Nambu-Goto string action can be related to an integrable deformation of a free theory. The scattering of excitations on the two-dimensional worldsheet of the string is then very simple, given by a pure phase. In this talk I will consider the setup of a membrane in flat space. I will analyse the dynamics of excitations on the three-dimensional worldvolume of the membrane, and also compactify the theory on a circle. I will present the perturbative S-matrix, compare with the Nambu-Goto case, and discuss the integrability of the model.

Speaker: Fiona Seibold

12:40 Lunch

12 Evidence for a four-dimensional N = 1 integrable quiver in massive type IIA supergravity

We examine a newly discovered parametric family of backgrounds in massive type IIA supergravity that contains a warped AdS5 factor. This family is the dual gravity description of four-dimensional quivers with N=1 supersymmetry. We are interested in the status of classical integrability in these theories, and we show that there exists a single choice of solutions that is special, while all other choices lead to nonintegrable quivers and chaotic string motion. By focusing on this special choice, we provide strong suggestive evidence for the integrability of the dual field theory based on analytic studies and extensive numerical analysis.

Speaker: José Manuel Penín

13 QCD form factors from large N chiral algebras

The collinear singularities of form factors in certain self-dual QCDs determine an abstract chiral algebra. In this talk I will realize an example concretely as the large N limit of an algebra of operators living on a 2d holomorphic surface defect. The construction goes via twisted holography for the type I topological string on a Calabi-Yau 5-fold related to twistor space. I will explain how this realization can be exploited to compute QCD form factors in flat space, and helicity amplitudes on a range of self-dual backgrounds. This is joint work with Kevin Costello and Keyou Zeng.

Speaker: Roland Bittleston

15:00 Break

16:00 Reception and Networking

Wednesday 17 July

14 Large charge and integrability

The large-charge expansion has in the last few years proven to be a powerful tool for analytically accessing strongly-coupled CFTs. When working in a sector of fixed and large global charge, it is often possible to write an EFT for this sector as an expansion controlled by inverse powers of the large charge. I will introduce the large-charge method and discuss its relationship and interactions with integrability.

Speaker: Susanne Reffert

15 Integrability from Chern-Simons Theory on Twistor Space

Insights into the origin of integrability are provided by two 4d gauge theoretic descriptions -- 4d Chern-Simons theory and self-dual Yang-Mills theory. Recently, both of these 4d models have been realised as children of a parent theory: 6d holomorphic Chern-Simons theory on twistor space. After a review of these topics, I will discuss our work extending this formalism.

Speaker: Lewis Cole

11:00 Break

16 Landscapes of integrable long-range spin chains

I will give an overview of the recent advances in understanding long-range integrable spin chains, focusing on a general construction that yields (q-)deformations of known models based on a solution of a Yang-Baxter equation. Even for the simplest sl_2-case, this construction generates two, mostly disconnected landscapes of models, with many intriguing properties. I will highlight those I believe to be most interesting to the IDD audience. based on https://arxiv.org/abs/2306.13066 and arxiv:2405.xxxxx (expected to appear before May 15th), both with Jules Lamers.

Speaker: Rob Klabbers

17 A generalized 4d Chern-Simons theory

We formally introduce a deformation of the 4d Chern-Simons theory, whose path integral takes the canonical symplectic form required by the non-Abelian localization method. The methodology is based on the Beasley-Witten construction applied to conventional 3d Chern-Simons theory. This opens the possibility for studying integrable field theories using geometric tools.

Speaker: David Schmidtt

12:40 Lunch

18 Poster Session

15:00 Break

19 A 3d topological-holomorphic integrable field theory from 2-groups

The 2d Wess-Zumino-Witten CFT is an integrable field theory that is known to host infinitely many conserved currents that obey the affine Kac-Moody algebra. This talk is based on the joint work https://arxiv.org/abs/2405.18625 with J. Liniado, where we introduced a 3d integrable field theory which can be thought of as a topological-holomorphic analogue of the 2d WZW CFT. A detailed analysis of its conserved chiral higher currents reveals the structure of a differential graded analogue of the 2-Kac-Moody algebra akin to Hennion-Faonte-Kapranov, and their higher holonomies have interesting geometric properties.

Speaker: Hank Chen

20 Kinematics and odd crossing in mixed flux AdS3/CFT2

Speaker: Bogdan Stefański, jr.

Thursday 18 July

21 Generalized cosets in exceptional geometry

Various extensions of Poisson-Lie T-duality have been studied recently. For the duality group O(D,D), the most general extension is known as the generalized T-duality of generalized cosets (extending dressing cosets). In this talk, considering the U-duality group E_{n(n)}, I will explain a construction of the generalized cosets in exceptional geometry, which we call exceptional generalized cosets. I will then discuss the generalized U-dualities among different exceptional generalized cosets. I will also explain how the exceptional generalized cosets can be used to study consistent truncations of maximal supergravities. This talk is based on works with Falk Hassler, arXiv:2311.12095 and ongoing work.

Speaker: Yuho Sakatani

11:00 Break

22 Classical deformations of Celestial Chiral Algebras

This talk is based on arXiv:2305.09451, arXiv:2403.18011 and work in progress. I will discuss several deformations of gravitational celestial chiral algebras which are closely related to $w_{1+\infty}$ and give bulk interpretations of the respective deformations. Some of these deformations arise naturally from a backreaction in self-dual Einstein gravity analogous to part of the recent top-down construction of Costello, Paquette and Sharma and I will highlight similarities and differences.

Speaker: Simon Heuveline

23 Symmetric Space Sine-Gordon Theories

Some aspects of Symmetric Space Sine-Gordon Theories will be reviewed:
their definitions, their properties and the peculiarity of their integrability structure.

Speaker: Marc Magro

12:40 Lunch

24 Yangians and R-matrices for cotangent Lie algebras

This talk is about a canonical quantization of Lie bialgebra structures on the loop algebra with coefficients in the semi-direct product of a simple complex Lie algebra and its dual. The quantization gives rise to twists of the natural analog of the Yangian for this algebra. The Yangian admits a meromorphic R-matrix, which relates its coproduct with a meromorphic coproduct. The construction of the Yangian is motivated by the fact that its representations can be interpreted as perturbative line operators in a 4d holomorphic topological gauge theory. This talk is based on the following joint work with Wenjun Niu: arXiv:2405.19906.

Speaker: Raschid Abedin

25 Integrability in twist-deformed SYM

Maximally supersymmetric Yang-Mills theory (SYM) in four dimensions is famously integrable, and AdS/CFT dual to the AdS5 superstring. The latter string admits a varied landscape of integrable Yang-Baxter deformations, which are conjectured to correspond to certain noncommutative deformations of SYM on the field theory side. Recently a large number of these twist-noncommutative deformations of SYM were explicitly constructed, making it possible to investigate their integrability, and ultimately perform precision tests of holography in this novel setting. I will consider deformations based on Cartan generators, where restricting to R symmetry gives the famous real beta deformation of SYM, but adding in Lorentz generators we get interesting new models. The simplest of these is an angular dipole deformation of SYM, which admits a class of gauge invariant operators whose two-point functions can be determined from a twisted integrable spin chain, at least as long as we restrict ourselves to the spacetime plane not touched by the deformation. This twisted structure precisely matches the one known for the conjectured dual string, providing a strong check of the conjectured duality. I will then discuss how integrable spin chains may be realized when considering operators at general positions in angular dipole deformed SYM, and comment on attempts to extrapolate this story to the analogous fully spacetime-noncommutative Lorentz deformation.

Speaker: Stijn van Tongeren

15:00 Break

26 Scattering on self-dual black holes

Tree-level graviton scattering amplitudes provide an on-shell model for wave-wave scattering in general relativity, but computing them with traditional perturbative methods is hard due to the non-polynomial nature of the Einstein-Hilbert action. This is particularly true for the study of graviton scattering in curved spacetimes, like black holes, which remains an extremely difficult problem. In this talk, I will discuss a simplification of this problem: graviton scattering on a self-dual black hole (in particular, a self-dual Taub-NUT space). This lets us bring powerful integrability methods to bear while still exhibiting the non-linear and non-perturbative hallmarks of 'real world' graviton scattering on black holes.

Speaker: Tim Adamo

27 Rotating strings and anomalous dimensions in TTbar deformation

We consider certain rigidly rotating closed string configurations in an asymptotically non-AdS string background. The string background is a deformation of AdS_3 × M_7 with NSNS two-from B field. It interpolates between AdS_3 and asymptotically linear dilaton IR × S^1 × IR spacetime (times the internal compact manifold M_7). In the long string sector the deformation is dual to a single trace TTbar deformed symmetric product theory. We compute the quantity E −J for certain rotating folded and cusped closed strings where E is the energy and J is the angular momentum of the strings. In the two dimensional CFT dual to string theory on AdS_3 (times M_7) it gives the anomalous dimensions of certain twist two and higher operators. We discuss the structure of (large angular momentum J expansion) of E − J and comment on what it measures away from the CFT along the deformation in the coupling space. We also discuss the closely related cusp anomalous dimension of a light-like Wilson loop. We also give semiclassical results for the energy of certain non-spinning pulsating strings. The talk is based on my recent paper: arXiv:2404.16601[hep-th].

Speaker: Meseret Asrat

19:00 Conference Dinner

Friday 19 July

28 Supergravity backgrounds from λ-deformations

In this talk, I will discuss the construction of two supersymmetric solutions of type-II supergravity based on the λ-deformed σ-models for SL(2,R) and SU(2). In the absence of deformation, they describe near-horizon limits of NS1 and NS5 brane intersections and both are 1/2-supersymmetric. When the deformation is turned on, supersymmetry breaks by half and both backgrounds preserve 8 supercharges.

Speaker: Georgios Itsios

11:00 Break

29 The Hagedorn temperature for integrable gauge theories

I discuss recent progress in computing the Hagedorn temperature at strong coupling for N=4 SYM and ABJM theory.

Speaker: Joseph Minahan

12:20 Closing Remarks

12:40 Lunch

14:00 Free Discussion