Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled (1+1)-dimensional principal chiral sigma models. The $SU(N)\times SU(N)$ principal chiral sigma model in 1+1 dimensions is integrable, asymptotically free and has massive excitations. We calculate all the form factors and two-point correlation functions of the Noether current and energy-momentum tensor, in 't~Hooft's large-$N$ limit (some form factors can be found even at finite $N$). We use these new form factors to calculate physical quantities in (2+1)-dimensional Yang-Mills theory, generalizing previous $SU(2)$ results from Orland to $SU(N)$. The anisotropic gauge theory is related to standard isotropic one by a Wilsonian renormalization group with ellipsoidal cutoffs in momentum. We calculate quantum corrections to the effective action of QED and QCD, as the theory flows from isotropic to anisotropic. The exact principal chiral sigma model S-matrix is also used to examine the spectrum of (1+1)-dimensional massive Yang Mills theory.
We explore two distinct methods to introduce integrable defects in a family of integrable sigma-models known as Yang-Baxter models. The first method invokes a modified monodromy matrix encoding an integrable defect separating two integrable systems. As an example we construct integrable defects in the ultralocal version of the $S^2$ Yang-Baxter model or 2d Fateev sausage model. The second method is based on the so-called "frozen" Bäcklund transformations. Lifting the construction to the Drinfel'd double, we show how defect matrices can be constructed for inhomogeneous Yang-Baxter models. We pr…
Integrable spin chains in twisted maximally supersymmetric Yang-Mills theory
Instituto Galego de Física de Altas Enerxías (IGFAE) and Departamento de Física de Partículas, Universidade de Santiago de Compostela（加利西亚高能物理研究所和圣地亚哥德孔波斯特拉大学粒子物理系）；Institut für Physik, Humboldt-Universität zu Berlin（柏林洪堡大学物理研究所）
A common approach to the quantization of integrable models starts with the formal substitution of the Yang-Baxter Poisson algebra with its quantum version. However it is difficult to discern the presence of such an algebra for the so-called non-ultralocal models. The latter includes the class of non-linear sigma models which are most interesting from the point of view of applications. In this work, we investigate the emergence of the Yang-Baxter Poisson algebra in a non-ultralocal system which is related to integrable deformations of the Principal Chiral Field.
The 2D $\mathcal{N}=(2,2)^*$ supersymmetric Yang-Mills theory can be obtained from the 2D $\mathcal{N}=(4,4)$ theory with a twisted mass deformation. In this paper we construct the gravity dual theory of the 2D $\mathcal{N}=(2,2)^*$ supersymmetric $U(N)$ Yang-Mills theory at the large $N$ and large 't Hooft coupling limit using the 5D gauged supergravity. In the UV regime, this construction also provides the gravity dual of the 2D $\mathcal{N}=(2,2)^*$ $U(N)$ topological Yang-Mills-Higgs theory. We propose a triality in the UV regime among integrable model, gauge theory and gravity, and we mak…
Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems
（1）四维1 \leq N \leq 4超对称Yang-Mills理论简介，包括粒子和场的内容，N=1和N=2超场方法以及一般不变拉格朗日量的构造;（II）回顾N=2超杨-米尔斯的全纯性和对偶性，Seiberg-Witten理论及其用Riemann曲面表示的形式;（III）介绍了力学Hamilton可积系统，如与一般李代数相关的Toda和Calogero-Moser系统，综述了最近构造的扭曲和非扭曲椭圆Calogero-Moser系统的带谱参数的拉克斯对;（IV）一般规范代数的Seiberg-Witten理论和伴随超多重态在椭圆Calogero-Moser可积系统中的最新解的评述。
In this short proceedings we discuss some of the results obtained in [1]. Integrable deformations enlarge the landscape and understanding of integrable models and its algebraic structures like quantum groups. In this short proceedings, we will review the one-loop renormalisation group analysis of an integrable deformation known as the Yang-Baxter Wess-Zumino model. This classically integrable model shows a striking stability under one-loop renormalisation. In addition, we show how Poisson-Lie T-duality, a generalisation of T-duality that is closely intertwined with integrable deformations, is …
The maximally supersymmetric Yang-Mills theory in four-dimensional Minkowski space is an exceptional model of mathematical physics. Even more so in the planar limit, where the theory is believed to be integrable. In particular, the tree-level scattering amplitudes were shown to be invariant under the Yangian of the superconformal algebra psu(2,2|4). This infinite-dimensional symmetry is a hallmark of integrability. In this dissertation we explore connections between these amplitudes and integrable models. Our aim is to lay foundations for an efficient integrability-based computation of amplitu…
We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle $R$-matrices also contains non-reducible 3-particle $R$-matrices. The corresponding modified Yang-Baxter equations are solved and an expression for the transfer matrix is found as a normal ordered exponential of a (non-local) Hamiltonian.
Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation
Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University（莫斯科国立大学理论物理与数学物理研究所）；National Research University Higher School of Economics（国立高等经济大学）；National Research Centre ”Kurchatov Institute”（库尔恰托夫国家研究中心）；Institute for Information Transmission Problems RAS (Kharkevich Institute)（俄罗斯科学院信息传输问题研究所（哈尔凯维奇研究所））；Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）
We consider a special class of quantum non-dynamical $R$-matrices in the fundamental representation of ${\rm GL}_N$ with spectral parameter given by trigonometric solutions of the associative Yang-Baxter equation. In the simplest case $N=2$ these are the well-known 6-vertex $R$-matrix and its 7-vertex deformation. The $R$-matrices are used for construction of the classical relativistic integrable tops of the Euler-Arnold type. Namely, we describe the Lax pairs with spectral parameter, the inertia tensors and the Poisson structures. The latter are given by the linear Poisson-Lie brackets for th…
Integrable sigma model with generalized $\mathcal{F}$ structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model
The classical Yangian symmetry of Auxiliary Field Sigma Models
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；High Energy Physics Research Unit, Faculty of Science Chulalongkorn University（朱拉隆功大学理学院高能物理研究单元）；Department of Physics, Northeastern University（东北大学物理系）；The NSF Institute for Artificial Intelligence and Fundamental Interactions（美国国家科学基金会人工智能与基本相互作用研究所）；School of Mathematics and Physics, University of Queensland（昆士兰大学数学与物理学院）
We propose a construction of 1+1 integrable Heisenberg-Landau-Lifshitz type equations in the ${\rm gl}_N$ case. The dynamical variables are matrix elements of $N\times N$ matrix $S$ with the property $S^2={\rm const}\cdot S$. The Lax pair with spectral parameter is constructed by means of a quantum $R$-matrix satisfying the associative Yang-Baxter equation. Equations of motion for ${\rm gl}_N$ Landau-Lifshitz model are derived from the Zakharov-Shabat equations. The model is simplified when ${\rm rank}(S)=1$. In this case the Hamiltonian description is suggested. The described family of models…
The BCFW recursion relation in $\mathcal{N}=4$ super-Yang-Mills theory is solved using Yang-Baxter $R$-operators in the NMHV sector. Explicit expressions for $\mathcal{R}$-invariants are obtained in terms of the chains of $R$-operators acting on an appropriate basic state.
