Integrability in Gravity from Chern-Simons Theory

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.

41 pages

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Cited by in corpus (2)

• Gauging The Diamond: Integrable Coset Models from Twistor Space
• Integrable Deformations of the Breitenlohner-Maison Model from 4d Chern-Simons Theory