标题： 来自四维 Chern-Simons 理论的可积 sigma 模型的 1-圈重正化群可容性 显示英文标题

标题： 1-loop renormalisability of integrable sigma-models from 4d Chern-Simons theory

摘要： 已经构造了大量可积的二维σ模型族，部分动机是弦世界面上可积性的实用性。 很自然地会问这些理论在量子水平上是否是可重整化的，并且它们是否定义了量子可积场论。 通过考虑例子，一个民间定理浮现出来：经典的可积σ模型总是至少在一环阶上表现出可重整性。 我们对Costello和Yamazaki在4维Chern-Simons理论的表面缺陷上构建的大类模型证明了这个定理。 我们推导出“扭曲1形式”（一个区分不同二维模型的4维耦合常数）的流，证实了早期的猜想并扩展了先前的结果。 我们的方法是通用的，利用二维可积模型在Lax联络下的UV发散的“普适”形式，并用4维Chern-Simons的语言重新解释这一结果。 这些结果同样适用于有理、三角和椭圆模型。 显示英文摘要

摘要： Large families of integrable 2d sigma-models have been constructed at the classical level, partly motivated by the utility of integrability on the string worldsheet. It is natural to ask whether these theories are renormalisable at the quantum level, and whether they define quantum integrable field theories. By considering examples, a folk theorem has emerged: the classically integrable sigma-models always turn out to be renormalisable, at least at 1-loop order. We prove this theorem for a large class of models engineered on surface defects in the 4d Chern-Simons theory by Costello and Yamazaki. We derive the flow of the 'twist 1-form' (a 4d coupling constant that distinguishes different 2d models), proving earlier conjectures and extending previous results. Our approach is general, using the 'universal' form of 2d integrable models' UV divergences in terms of their Lax connection and reinterpreting the result in the language of 4d Chern-Simons. These results apply equally to rational, trigonometric and elliptic models.