Integrability in Lower Dimensional AdS/CFT

Virtual Workshop

CONTACT FOR ANY QUERIES: a dot torrielli hat surrey dot ac dot uk

HMI online Workshop, 17-20 August 2021

Scientific Program

Recent years have seen an extraordinary development in the field of supersymmetric integrable systems. These developments were particularly driven by the discovery of integrable structures in theories that arise in the AdS/CFT correspondence. So far, most results have been derived for the prototypical example of the AdS/CFT correspondence; the duality between type IIB string theory on AdS5xS5 and 4d SYM. Here the discovery of an exactly integrable scattering matrix governing the dynamics of massive excitations realized by superstrings propagating has lead to astounding results, such as an exact description of spectrum of anomalous dimensions in the dual field theory.

In the lower dimensional instances of the AdS/CFT correspondence integrability is at work in a similar fashion as in the five-dimensional case. However, for three and two dimensional AdS spaces, new features arise: massless modes make their appearance in the scattering problem, and the issue of massless S-matrices and the associated Thermodynamic Bethe Ansatz (TBA) take centre stage. The appropriate interpretation is traditionally that of a renormalisation group flow between critical theories, with the ground-state TBA providing a measure of the effective central charge along the flow. Some of the models generated from string theory in this way are very special and do not admit a standard treatment, such as those who exhibit the absence of a reference state and display very peculiar properties of their transfer matrices.

The aim of the workshop will be to bring together some of the world-experts in AdS/CFT integrability, alongside researchers with wide expertise in massless scattering and thermodynamic analysis, working at the interface between integrable systems and conformal field theory.

Location

Online (Zoom) hosted by Trinity College Dublin

Speakers

I. Aniceto (Univ. of Southampton)
C. Dunning (Univ. of Kent)
P. Fendley (Oxford University)
R. Nepomechie (Univ. of Miami)
P. Ryan (TCD/HMI)
H. Saleur (Saclay and USC)
F. Seibold (ETH)
B. Stefanski (City, Univ. of London)
D. Volin (Uppsala U. and Stockholm U.)

Registration

The Zoom link will be circulated in due course, or can be requested by emailing: a dot torrielli hat surrey dot ac dot uk

Organizers

Marius de Leeuw (TCD/HMI)
Juan Miguel Nieto Garcia (Univ. of Surrey)
Ana Retore (TCD/HMI)
Alessandro Torrielli (Univ. of Surrey)

Sponsors

The Hamilton Mathematics Institute
The Simons Foundation
Science Foundation Ireland
The Royal Society
EPSRC
GATIS+

SCHEDULE (please check regularly for updates)

Tuesday 17 14:00 - 17:00 UK time [Fendley, Dunning and Nepomechie]

Wednesday 18 14:00 - 17:00 UK time [Aniceto, Seibold and Saleur]

Thursday 19 [no talks]

Friday 20 14:00 - 17:00 UK time [Ryan, Volin and Stefanski]

Each talk will be 40-45 minutes

TITLES OF THE TALKS:

Paul Fendley: "Free Fermions and Parafermions"

Clare Dunning: "Taming Monsters"

Rafael Nepomechie: "Solving a black-hole spin chain"

Ines Aniceto: "AdS/CFT inspired Massive-Massless interactions in Integrable Field Theories"

Fiona Seibold: "S matrices for quantum-deformed superstrings"

Hubert Saleur: "The O(n) and Q-state Potts model CFTs in 2d: the conclusion of a long story?"

Paul Ryan: "Separation of Variables: from wave functions to correlators in high rank integrable spin chains"

Dmytro Volin: "Bethe Algebras and Fused Flags" *

Bogdan Stefanski: "String theory on AdS3 X S3 X T4"

ABSTRACTS:

*Dmytro Volin: Bethe Algebras and Fused Flags

Our goal is to offer a “good” description for the algebra of commuting charges in an integrable model (Bethe algebra). This takes us to realise the role of the Langlands dual of the symmetry algebra: it naturally acts on the extended family of Baxter Q-functions giving them a geometrical interpretation of a set of Plucker coordinates on the flag G/B that enjoy, as functions of spectral parameter, non-trivial fusion relations. Demanding analytic properties (aka analytic Bethe Ansatz) to be compatible with fusion relations is a way to describe Bethe algebra which is more accurate and often more efficient than Bethe equations/Baxter equations/(unextended) QQ-systems. Given covariance with respect to the Langlands dual, construction of T-functions becomes a simple exercise and we can offer solutions for most types of T-systems known in the literature (e.g. like those for Dynkin TBA’s).

As an example, we take rational spin chains but the formalism is universal and is a feature of (twisted) affine Lie algebras rather than of a physical system. For simplicity, we shall only write formulas assuming the simply-laced ADE case during the talk and provide explicit examples from A-series (understood a while ago) and D-series (that was extensively studied last year).

Based on 2008.10597, 2104.04539 and a forthcoming publication with S.Ekhammar.

Talk Paul Fendley

zoom_0.mp4

Talk Rafael Nepomechie

zoom_1.mp4

Talk Ines Aniceto

zoom_0 2.mp4

Talk Fiona Seibold

zoom_1 2.mp4

Slides Hubert Saleur

Saleur.pdf

Talk Paul Ryan

zoom_1 kopie.mp4

Talk Dima Volin

zoom_2.mp4

Talk Bogdan Stefanski

zoom_3.mp4

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