54 citations · 647 across the 25 of their papers we have counts for
28 papers
The Magic Renormalisability of Affine Gaudin Models
Falk Hassler, Sylvain Lacroix, Benoit Vicedo
We study the renormalisation of a large class of integrable -models obtained in the framework of affine Gaudin models. They are characterised by a simple Lie algebra $\mathfrak{…
On a class of conformal -models and their chiral Poisson algebras
Sylvain Lacroix
In this paper, we study conformal points among the class of -models. The latter are -models formulated in terms of a current Poisson algebra, whose Lie-theoretic de…
Integrable sigma models at RG fixed points: quantisation as affine Gaudin models
Gleb A. Kotousov, Sylvain Lacroix, Jörg Teschner
The goal of this paper is to make first steps towards the quantisation of integrable non-linear sigma models using the formalism of affine Gaudin models, by approaching these theor…
Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation
Ilija Buric, Sylvain Lacroix, Jeremy A. Mann +2
We continue the exploration of multipoint scalar comb channel blocks for conformal field theories in 3D and 4D. The central goal here is to construct novel comb channel cross ratio…
4-dimensional Chern-Simons theory and integrable field theories
Sylvain Lacroix
These lecture notes concern the semi-holomorphic 4d Chern-Simons theory and its applications to classical integrable field theories in 2d and in particular integrable sigma-models.…
Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
Ilija Buric, Sylvain Lacroix, Jeremy A. Mann +2
It was recently shown that multi-point conformal blocks in higher dimensional conformal field theory can be considered as joint eigenfunctions for a system of commuting differentia…
Gaudin Models and Multipoint Conformal Blocks: General Theory
Ilija Buric, Sylvain Lacroix, Jeremy Mann +2
The construction of conformal blocks for the analysis of multipoint correlation functions with local field insertions is an important open problem in higher dimensional con…
Integrable -Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
Sylvain Lacroix, Benoit Vicedo
We construct the actions of a very broad family of 2d integrable -models. Our starting point is a universal 2d action obtained in [arXiv:2008.01829] using the framework of Coste…
Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
B. Hoare, S. Lacroix
A large class of integrable deformations of the Principal Chiral Model, known as the Yang-Baxter deformations, are governed by skew-symmetric R-matrices solving the (modified) clas…
RG flows of integrable -models and the twist function
François Delduc, Sylvain Lacroix, Konstantinos Sfetsos +1
In the study of integrable non-linear -models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist functio…
New integrable coset sigma models
Gleb Arutyunov, Cristian Bassi, Sylvain Lacroix
By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of copies of a Li…
From Gaudin Integrable Models to -dimensional Multipoint Conformal Blocks
Ilija Buric, Sylvain Lacroix, Jeremy A. Mann +2
In this work we initiate an integrability-based approach to multipoint conformal blocks for higher dimensional conformal field theories. Our main observation is that conformal bloc…
Integrable deformations of coupled sigma-models
Cristian Bassi, Sylvain Lacroix
We construct integrability-preserving deformations of the integrable -model coupling together copies of the Principal Chiral Model. These deformed theories are obtained usin…
Ultralocal Lax connection for para-complex -cosets
Francois Delduc, Takashi Kameyama, Sylvain Lacroix +2
We consider -models on para-complex -cosets, which are analogues of those on complex homogeneous target spaces considered recently by D. Bykov. For these models, w…
A unifying 2d action for integrable -models from 4d Chern-Simons theory
Francois Delduc, Sylvain Lacroix, Marc Magro +1
In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern-Simons theory, we derive a simple and unifying two-dimension…
Constrained affine Gaudin models and diagonal Yang-Baxter deformations
Sylvain Lacroix
We review and pursue further the study of constrained realisations of affine Gaudin models, which form a large class of two-dimensional integrable field theories with gauge symmetr…
Assembling integrable sigma-models as affine Gaudin models
Francois Delduc, Sylvain Lacroix, Marc Magro +1
We explain how to obtain new classical integrable field theories by assembling two affine Gaudin models into a single one. We show that the resulting affine Gaudin model depends on…
Integrable coupled sigma-models
Francois Delduc, Sylvain Lacroix, Marc Magro +1
A systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined. It is based on the recent interpretation of integrabl…
Three-parameter integrable deformation of Z_4 permutation supercosets
Francois Delduc, Ben Hoare, Takashi Kameyama +2
A three-parameter integrable deformation of permutation supercosets is constructed. These supercosets are of the form where is the bos…
Integrable models with twist function and affine Gaudin models
Sylvain Lacroix
This thesis deals with a class of integrable field theories called models with twist function. The main examples of such models are integrable non-linear sigma models, such as the…
Cubic hypergeometric integrals of motion in affine Gaudin models
Sylvain Lacroix, Benoit Vicedo, Charles A. S. Young
We construct cubic Hamiltonians for quantum Gaudin models of affine types . They are given by hypergeometric integrals of a form we recently conjectured in a…
Affine Gaudin models and hypergeometric functions on affine opers
Sylvain Lacroix, Benoit Vicedo, Charles A. S. Young
We conjecture that quantum Gaudin models in affine types admit families of local higher Hamiltonians, labelled by the (countably infinite set of) exponents, whose eigenvalues are g…
Local charges in involution and hierarchies in integrable sigma-models
Sylvain Lacroix, Marc Magro, Benoit Vicedo
Integrable -models, such as the principal chiral model, -coset models for and their various integrable deformations, are examples o…
Cyclotomic Gaudin models, Miura opers and flag varieties
Sylvain Lacroix, Benoit Vicedo
Let be a semisimple Lie algebra over . Let be a diagram automorphism whose order divides . We…