近日，英国斯旺西大学的Peter Weck及其研究团队取得一项新进展。经过不懈努力，他们揭示源于Chern-Simons理论的引力中的可积性。相关研究成果已于2024年10月9日在国际知名学术期刊《高能物理杂志》上发表。

本文为引力理论中的可积性提供了新的视角。研究人员展示了如何通过四维Chern-Simons理论的边界动力学，来描述广义相对论中的静态轴对称部分。

此方法有望简化广义相对论和高维超引力理论中解的生成方法。所提出的四维Chern-Simons理论通过在谱平面上引入时空依赖的分支割线，推广了适用于平坦空间可积模型的理论。

此外，研究人员还与扭子空间的可积性方法相联系，展示了四维Chern-Simons理论中的分支割线缺陷，是如何从六维Chern-Simons理论的离散约化中产生的。

附：英文原文

Title: Integrability in gravity from Chern-Simons theory

Author: Cole, Lewis T., Weck, Peter

Issue&Volume: 2024-10-09

Abstract: This paper presents a new perspective on integrability in theories of gravity. We show how the stationary, axisymmetric sector of General Relativity can be described by the boundary dynamics of a four-dimensional Chern-Simons theory. This approach shows promise for simplifying solution generating methods in both General Relativity and higher-dimensional supergravity theories. The four-dimensional Chern-Simons theory presented generalises those for flat space integrable models by introducing a space-time dependent branch cut in the spectral plane. We also make contact with twistor space approaches to integrability, showing how the branch cut defects of four-dimensional Chern-Simons theory arise from a discrete reduction of six-dimensional Chern-Simons theory.

DOI: 10.1007/JHEP10(2024)080

Source: https://link.springer.com/article/10.1007/JHEP10(2024)080