Abstracts

Introductory talks

TBA

Alessandro Sfondrini

TBA

Integrable sigma models

Ben Hoare

In this introductory talk, we will review some of the key ideas behind classical integrability in 2-dimensional sigma models and the 4d Chern-Simons approach to charting out the landscape of these theories. We will highlight how both worldsheet dualities (such as T-duality) and integrable deformations (such as the Yang-Baxter deformation) arise in this framework. Time-permitting, we will finish with a brief discussion of extending the construction to higher dimensions.

Research talks

QQ-Systems for opers with regular singularity

Henry Bittleston (University of York)

The ODE/IM correspondence provides an unexpected connection between the structure of certain integrable quantum field theories (IQFTs) and the spectral theory of ODEs. In recent years, this correspondence has been linked, via geometric Langlands, to a conjectural description of the spectrum of affine Gaudin models in terms of functions on a class of connections known as opers.

In this talk, I will begin by reviewing two mechanisms through which the spectra of these IQFTs can be recovered from the spectral data of opers. The first describes the spectrum and structure of the Q-operator through a radial connection problem, while the second uses the quasi-canonical form of an oper to construct local spectral data. Following this, I will introduce a novel family of connection coefficients relating perturbative solutions near regular singularities to solutions arising from this quasi-canonical form. These coefficients satisfy a QQ-type system, enabling the construction of non-local spectral data even when no natural radial connection problem exists. Time permitting, I will interpret these connection coefficients through known examples of the ODE/IM correspondence and discuss possible extensions of the construction to higher-rank algebras.

Spacial and Temporal Entanglement Measures in Quantum Field Theory

Olalla Castro Alvaredo (City st. George's, University of London)

This talk will start with an introduction to Entanglement Measures. I will explain what they are, what they are good for, and how they may be computed. I will review some results which are well known in the many-body quantum systems/quantum field theory/high energy communities and highlight their importance and applications. In the second part I will present some more technical details about a particular approach to these problems which is based on the use of branch point twist fields. Time permiting, I will introduce the most recent entanglement measure that has been computed within this approach, that is a temporal entanglement measure, where the role traditionally played by the system size (space) is now played by time. This last part is inspired by my recent preprint 2603.20765.

From Higher to Raviolo Chiral Algebras

Laura O. Felder (Hertfordshire University)

Besides their rich intrinsic mathematical structure, which is studied in its own right, vertex algebras as originally introduced by Borcherds present a highly productive tool for describing two-dimensional CFTs.

By introducing the concept of a chiral algebra on an algebraic curve, Beilinson and Drinfeld have provided a reformulation that centres around the similarity between the operator product expansion and the Jacobi identity for Lie algebras. Concretely, a chiral algebra is a Lie algebra in the category of D-modules. While for vertex algebras a generalisation to higher dimension seems very difficult, higher chiral algebras can be defined without major complications. Via a polysimplicial model of the derived sections on configuration spaces, in joint work with Zhengping Gui and Charles Young, we have shown that the fundamental example reassembles a Lie-infinity algebra.

Motivated by holomorphic-topological twists of super Yang-Mills theories, together with Keyou Zeng, our aim is to construct a similar description for such QFTs in analogy to the notion of raviolo vertex algebras introduced by Alfonsi, Kim, Young.

TBA

Tamara Grava (University of Bristol)

TBA

Auxiliary Field deformation of E-Model

Parita R. Shah (Durham University)

Auxiliary field sigma models (AFSMs) provide a large class of integrable deformations of two-dimensional field theories, including TT̄, root-TT̄, and their higher-spin generalizations, obtained by coupling an algebraic auxiliary field to a parent integrable model. We show that these deformations admit a uniform first-order formulation as E-models on a Drinfel'd double, for a general interaction function. Constructing a Lax connection for the deformed model, we find that integrability is guaranteed whenever the undeformed seed E-model is itself integrable, subject to a simple constraint on the interacting function. This reproduces known results for auxiliary field deformations of the PCM, Yang-Baxter, and λ-models within a single framework. I will further talk about a dual µ-frame formulation of these models, related to the parent AFSM by a Legendre transform in the spirit of the Courant-Hilbert construction, and describe how its Lax structure translates to the level of the Drinfel'd double.

Higher-level Universal Reflection Equations

Robert Weston (Heriot-Watt University)

Reflection equations in the literature are typically for zero level.

In this talk I will describe joint work with Bart Vlaar in which we use the trigonometric universal K-matrix to derive universal, twisted reflection equations for  quantum affine algebras. These equations explicitly involve the level, and make sense for both non-zero level and zero level representations.