List of Titles and Abstracts

Niklas Beisert: Contractions of Integrability Algebras and R-matrices

A large class of R-matrices satisfying the (classical/quantum) YBE is provided by the established tools of classical and quantum algebra (quasi-triangular Lie bialgebras, quantum affine algebras, ...). In particular, R-matrices of difference form based on semi-simple Lie algebras (as well as twists thereof) are well understood. However, there are also prominent examples of R-matrices which do not belong to this class.
In this talk I propose to apply algebraic contraction to semi-simple Lie algebras in order to construct interesting new algebras and R-matrices.
We consider the simple example of the contraction of SO(4) to ISO(3).
When applied to the quantum algebra structures of Uq(SO(4)) one can obtain (an extension of) the kappa-deformed Poincare algebra including an explicit expression for its R-matrix.
This example can be generalised to explain the algebraic origin of Shastry's R-matrix for the one-dimensional Hubbard model which is also encountered as the worldsheet scattering matrix in the AdS/CFT context.
This involves promotion to an affine algebra, adding supersymmetry as well as performing a curious reduction of the non-semi-simple structure of the affine algebra.
 

Riccardo Borsato: Yang-Baxter deformations in AdS/CFT: towards an integrability description of their spectrum

Homogeneous Yang-Baxter deformations are interesting options to deform sigma-models while preserving their classical integrability. Particularly promising is their application to integrable string sigma-models that appear in instances of the AdS/CFT correspondence. An exciting possibility, in fact, is to obtain exact results for non-conformal gauge theories with little or no supersymmetry, that are understood as deformations of N=4 SYM and should be holographically dual to Yang-Baxter deformations of AdS_5 x S^5. I will review the motivations, the challenges and the proposed solutions within this ongoing program.

Marius de Leeuw: Integrability and long-range interactions

I will give an overview on recent approaches to solving the Yang-Baxter equation. I will discuss some recent results and progress. I'll touch upon some open problems with a focus on potential applications to the AdS/CFT correspondence. In particular I'll discuss integrable models with long-range interactions.  

Sergey Frolov: Towards the mirror TBA for the mixed-flux $AdS_3\times S_3times T_4$ superstring I

We review some properties of the mixed-flux $AdS_3\times S_3times T_4$ superstring, introduce a deformed Zhukovsky variables and discuss their analytic properties.

Falk Hassler: The Generalized Geometry of Integrable σ-modelstba

Many integrable σ-models are based on highly symmetric target space geometries like group manifolds or cosets. On the other hand, they frequently admit integrability-preserving deformations which result in new, very complicated target space geometries mixing the metric and the B-field. As I will argue, this contrast is resolved by transitioning to generalized geometry, where many of the known deformations (perhaps even
all?) are captured by generalized coset spaces. The latter have many intriguing properties. Perhaps the most remarkable one is that they underlie all known generalized dualities in string theory. In my talk, I will discuss their construction, scope, and application to compute β-functions.

Ben Hoare: Trigonometric and elliptic deformations of strings on AdS3 backgrounds

I will review recent developments and open challenges in the construction and quantization of trigonometric and elliptic deformations of strings on AdS3 backgrounds.

Ctirad Klimčík: Point particle E-models

We show that the same algebraic data that permit to construct the Lax pair and the r-matrix of an integrable non-linear σ-model in 1 + 1 dimensions can be also used for the construction of Lax pairs and of r-matrices of several other non-trivial integrable theories in 1 + 0 dimension. We call those new integrable theories the point particle E-models, we describe their structure and give their physical
interpretation. We work out in detail the point particle E-models associated to the bi-Yang-Baxter deformation of the SU(N) principal chiral model. In particular, for each complex flag manifold we thus obtain a two-parameter family of integrable models living on it.

Gleb Kotousov: Studying the spectral problem in non-rational 2D CFTs via the scaling limit of critical, integrable, 1+1 dimensional spin chains.

The talk concerns the problem of computing the spectrum of scaling dimensions in 2D CFT. We focus on the case of non-rational models, where there is a continuous component in the spectrum. We illustrate and discuss the challenges of analyzing such theories on the example of the 2D Euclidean black hole CFT. It is argued that an effective way of obtaining the exact solution is through the study of the scaling limit of critical, integrable 1+1 dimensional lattice models.

Nat Levine: 1-loop renormalisability of a class of integrable sigma-models

It has been conjectured that classically integrable 2d sigma-models are stable under 1-loop renormalisation. I will present a proof of this conjecture, which applies to a large class of theories: those that can be engineered on surface defects in 4d Chern-Simons theory.
The first step is to show that integrable sigma-models’ 1-loop divergences take a ‘universal’ form in terms of the classical Lax connection. Writing this result in the language of 4d Chern-Simons, one learns that the 4d coupling constant (the 'twist function') can absorb all the 1-loop divergences. This implies 1-loop renormalisability and proves a particular flow of the twist function, previously conjectured by Delduc, Lacroix, Sfetsos and Siampos.
 

Marc Magro: 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.

Stefano Negro: A new representation of minimal form factors in Integrable QFTs

In this talk, I will present a new representation of the minimal form factors in integrable quantum field theories. This arises from a recent study of general TTbar-perturbed theories, where it was shown that the minimal form factors decompose into elementary building blocks. Here, focusing on the paradigmatic sinh-Gordon model, I will show that the standard integral representation of the minimal form factor can be expressed as a superposition of infinitely many elementary terms, each representing the minimal form factor of a generalised TTbar perturbation of the free fermion.

Davide Polvara: Towards the mirror TBA for the mixed-flux AdS3xS3xT4 superstring II

We propose solutions to the crossing equations of the mixed-flux AdS3xS3xT4 superstring.

Daniel Thompson: Integrable Deformations and Coset CFTs from Twistor Space

Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons in 6 dimensions. We provide the first complete description of this diamond for a multi-parameter 2d integrable model, which specialises to the λ-deformation at a certain point in parameter space. We further extend this approach to give a higher dimensional origin to G/H CFTs (with Lagrangian realisations as gauged-WZW models) as well as some of their (novel) intergrable deformations.

Arkady Tseytlin: Quantum supermembranes and AdS/CFT

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

Benoît Vicedo: tba

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