Deformed integrable models from holomorphic Chern-Simons theory

作     者：Yi-Jun He Jia Tian Bin Chen 

作者机构：School of PhysicsPeking UniversityBeijing 100871China Collaborative Innovation Center of Quantum MatterBeijing 100871China Center for High Energy PhysicsPeking UniversityBeijing 100871China Kavli Institute for Theoretical Sciences(KITS)University of Chinese Academy of SciencesBeijing 100190China 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2022年第65卷第10期

页      面：53-74页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China (Grant No. 11735001) supported by the National Youth Fund (Grant No. 12105289) the UCAS Program of Special Research Associate the Internal Funds of the KITS 

主　　题：integrable systems gauge field theories classical field theories 

摘      要：We study the approaches to two-dimensional integrable field theories via a six-dimensional(6 D) holomorphic Chern-Simons theory defined on twistor space. Under symmetry reduction, it reduces to a 4 D Chern-Simons theory, while under solving along fibres it leads to a four-dimensional(4 D) integrable theory, the anti-self-dual Yang-Mills or its generalizations. From both 4 D theories, various two-dimensional integrable field theories can be obtained. In this work, we try to investigate several twodimensional integrable deformations in this framework. We find that the λ-deformation, the rational η-deformation, and the generalized λ-deformation can not be realized from the 4 D integrable model approach, even though they could be obtained from the 4 D Chern-Simons theory. The obstacle stems from the incompatibility between the symmetry reduction and the boundary conditions. Nevertheless, we show that a coupled theory of the λ-deformation and the η-deformation in the trigonometric description could be obtained from the 6 D theory in both ways, by considering the case that(3, 0)-form in the 6 D theory is allowed to have zeros.