标题： 带有辅助场的4D Chern-Simons理论 显示英文标题

标题： 4D Chern-Simons theory with auxiliary fields

摘要： 辅助场sigma模型（AFSM）最近由费尔科和史密斯构造，它是主链路模型的变形，通过引入辅助场和任意单变量函数给出的势项实现的。 这个AFSM提供了一个无穷大的可积sigma模型族，包括原始的$T\overline{T}$-形变和根$T\overline{T}$-形变。 本文提出了一种带有辅助场的4维Chern-Simons（CS）理论。然后通过为规范场和辅助场施加适当的边界条件，从这个CS理论以及主链路模型的扭曲函数导出了AFSM。我们还通过扭曲函数的形变和边界条件的修改，得到了带Wess-Zumino项的AFSM。 显示英文摘要

摘要： The auxiliary field sigma model (AFSM) has recently been constructed by Ferko and Smith as deformations of the principal chiral model by including auxiliary fields and the potential term given by an arbitrary univariate function. This AFSM provides an infinite family of integrable sigma models including the original $T\overline{T}$-deformation and the root $T\overline{T}$-deformation. In this paper, we propose a 4D Chern-Simons (CS) theory with auxiliary fields. Then the AFSM is derived from this CS theory with the twist function for the principal chiral model by imposing appropriate boundary conditions for the gauge field and auxiliary fields. We also derive the AFSM with the Wess-Zumino term by deforming the twist function and modifying the boundary conditions.