Integrability in Gravity from Chern-Simons Theory

TL;DR

This paper links integrability in gravity to boundary dynamics of a four-dimensional Chern-Simons theory, offering a new framework that simplifies solution methods and connects to twistor space approaches.

Contribution

It introduces a novel four-dimensional Chern-Simons formulation for gravity integrability, generalizing existing models with space-time dependent branch cuts and connecting to six-dimensional theories.

Findings

Boundary dynamics of 4D Chern-Simons describe stationary axisymmetric gravity.

Generalization of flat space integrable models with space-time dependent branch cuts.

Connection established between 4D Chern-Simons defects and 6D reductions.

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.