Benoît Vicedo
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View article: Full universal enveloping vertex algebras from factorisation
Full universal enveloping vertex algebras from factorisation Open
We give a systematic construction of the symmetries, or observables in the vacuum sector, of a full conformal field theory on an arbitrary real two-dimensional conformal manifold $Σ$. Specifically, we construct a prefactorisation algebra o…
View article: 5d 2-Chern-Simons Theory and 3d Integrable Field Theories
5d 2-Chern-Simons Theory and 3d Integrable Field Theories Open
The 4-dimensional semi-holomorphic Chern-Simons theory of Costello and Yamazaki provides a gauge-theoretic origin for the Lax connection of 2-dimensional integrable field theories. The purpose of this paper is to extend this framework to t…
View article: Lagrangian Multiform for Cyclotomic Gaudin Models
Lagrangian Multiform for Cyclotomic Gaudin Models Open
We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on coadjoi…
View article: Universal First-Order Massey Product of a Prefactorization Algebra
Universal First-Order Massey Product of a Prefactorization Algebra Open
This paper studies the universal first-order Massey product of a prefactorization algebra, which encodes higher algebraic operations on the cohomology. Explicit computations of these structures are carried out in the locally constant case,…
View article: Lagrangian Multiform for Cyclotomic Gaudin Models
Lagrangian Multiform for Cyclotomic Gaudin Models Open
We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on coadjoi…
View article: 5d 2-Chern-Simons theory and 3d integrable field theories
5d 2-Chern-Simons theory and 3d integrable field theories Open
The $4$-dimensional semi-holomorphic Chern-Simons theory of Costello and Yamazaki provides a gauge-theoretic origin for the Lax connection of $2$-dimensional integrable field theories. The purpose of this paper is to extend this framework …
View article: Classical Yang–Baxter Equation, Lagrangian Multiforms and Ultralocal Integrable Hierarchies
Classical Yang–Baxter Equation, Lagrangian Multiforms and Ultralocal Integrable Hierarchies Open
We cast the classical Yang–Baxter equation (CYBE) in a variational context for the first time, by relating it to the theory of Lagrangian multiforms, a framework designed to capture integrability in a variational fashion. This provides a s…
View article: The magic renormalisability of affine Gaudin models
The magic renormalisability of affine Gaudin models Open
A bstract We study the renormalisation of a large class of integrable σ -models obtained in the framework of affine Gaudin models. They are characterised by a simple Lie algebra $$ \mathfrak{g} $$ and a rational twist function φ ( z ) wi…
View article: The magic renormalisability of affine Gaudin models
The magic renormalisability of affine Gaudin models Open
We study the renormalisation of a large class of integrable $σ$-models obtained in the framework of affine Gaudin models. They are characterised by a simple Lie algebra $\mathfrak{g}$ and a rational twist function $φ(z)$ with simple zeros,…
View article: Universal first-order Massey product of a prefactorization algebra
Universal first-order Massey product of a prefactorization algebra Open
This paper studies the universal first-order Massey product of a prefactorization algebra, which encodes higher algebraic operations on the cohomology. Explicit computations of these structures are carried out in the locally constant case,…
View article: Integrable Degenerate $$\varvec{\mathcal {E}}$$-Models from 4d Chern–Simons Theory
Integrable Degenerate $$\varvec{\mathcal {E}}$$-Models from 4d Chern–Simons Theory Open
We present a general construction of integrable degenerate $$\mathcal {E}$$ -models on a 2d manifold $$\Sigma $$ using the formalism of Costello and Yamazaki based on 4d Chern–Simons theory on $$\Sigma \times {\mathbb {C}}{P}^1$$ …
View article: Integrable degenerate $\mathcal E$-models from 4d Chern-Simons theory
Integrable degenerate $\mathcal E$-models from 4d Chern-Simons theory Open
We present a general construction of integrable degenerate $\mathcal E$-models on a 2d manifold $Σ$ using the formalism of Costello and Yamazaki based on 4d Chern-Simons theory on $Σ\times \mathbb{C}P^1$. We begin with a physically motivat…
View article: 3-Dimensional mixed BF theory and Hitchin’s integrable system
3-Dimensional mixed BF theory and Hitchin’s integrable system Open
The affine Gaudin model, associated with an untwisted affine Kac–Moody algebra, is known to arise from a certain gauge fixing of 4-dimensional mixed topological–holomorphic Chern–Simons theory in the Hamiltonian framework. We show that the…
View article: Chirality in 2d pAQFT
Chirality in 2d pAQFT Open
In this article, which builds upon the work done in our previous paper, the chiral aspects of 2dcft on globally hyperbolic Lorentzian manifolds are developed and explored within the perturbative algebraic quantum field theory (pAQFT) frame…
View article: Lorentzian 2D CFT from the pAQFT Perspective
Lorentzian 2D CFT from the pAQFT Perspective Open
We provide a detailed construction of the quantum theory of the massless scalar field on two-dimensional, globally hyperbolic (in particular, Lorentzian) manifolds using the framework of perturbative algebraic quantum field theory. From th…
View article: Classical Yang-Baxter equation, Lagrangian multiforms and ultralocal integrable hierarchies
Classical Yang-Baxter equation, Lagrangian multiforms and ultralocal integrable hierarchies Open
We cast the classical Yang-Baxter equation (CYBE) in a variational context for the first time, by relating it to the theory of Lagrangian multiforms, a framework designed to capture integrability in a variational fashion. This provides a s…
View article: Kondo line defects and affine Gaudin models
Kondo line defects and affine Gaudin models Open
A bstract We describe the relation between integrable Kondo problems in products of chiral SU(2) WZW models and affine SU(2) Gaudin models. We propose a full ODE/IM solution of the spectral problem for these models.
View article: Lorentzian 2d CFT from the pAQFT perspective
Lorentzian 2d CFT from the pAQFT perspective Open
We provide a detailed construction of the quantum theory of the massless scalar field on 2-dimensional, globally-hyperbolic (in particular, Lorentzian) manifolds using the framework of perturbative algebraic quantum field theory. From this…
View article: Integrable E-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
Integrable E-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects Open
We construct the actions of a very broad family of 2d integrable\n$\\sigma$-models. Our starting point is a universal 2d action obtained in\n[arXiv:2008.01829] using the framework of Costello and Yamazaki based on 4d\nChern-Simons theory. …
View article: 4D Chern–Simons theory and affine Gaudin models
4D Chern–Simons theory and affine Gaudin models Open
We relate two formalisms recently proposed for describing classical integrable field theories. The first (Costello and Yamazaki in Gauge Theory and Integrability, III, 2019) is based on the action of four-dimensional Chern–Simons theory in…
View article: Kondo line defects and affine Gaudin models
Kondo line defects and affine Gaudin models Open
We describe the relation between integrable Kondo problems in products of chiral $SU(2)$ WZW models and affine $SU(2)$ Gaudin models. We propose a full ODE/IM solution of the spectral problem for these models.
View article: Homotopical analysis of 4d Chern-Simons theory and integrable field theories
Homotopical analysis of 4d Chern-Simons theory and integrable field theories Open
This paper provides a detailed study of $4$-dimensional Chern-Simons theory on $\mathbb{R}^2 \times \mathbb{C}P^1$ for an arbitrary meromorphic $1$-form $ω$ on $\mathbb{C}P^1$. Using techniques from homotopy theory, the behaviour under fin…
View article: A unifying 2D action for integrable $$\sigma $$-models from 4D Chern–Simons theory
A unifying 2D action for integrable $$\sigma $$-models from 4D Chern–Simons theory Open
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-dimensional form for the action of many integrable $$\sigma $$ -mod…
View article: Cubic hypergeometric integrals of motion in affine Gaudin models
Cubic hypergeometric integrals of motion in affine Gaudin models Open
We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst themsel…
View article: Holomorphic Chern-Simons theory and affine Gaudin models
Holomorphic Chern-Simons theory and affine Gaudin models Open
We relate two formalisms recently proposed for describing classical integrable field theories. The first is based on the action of four-dimensional holomorphic Chern-Simons theory introduced and studied by Costello, Witten and Yamazaki. Th…
View article: Assembling integrable σ-models as affine Gaudin models
Assembling integrable σ-models as affine Gaudin models Open
A bstract 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 a parameter γ in such a way that the limit γ → 0…
View article: Integrable Coupled <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math> Models
Integrable Coupled Models Open
A systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined. It is based on the recent interpretation of integrable field theories as realizations of affine Gaudin models. I…