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.
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Acknowledgments
The authors would like to thank Ibrahima Bah, Roland Bittleston, Wei Bu, Ryan Cullinan, Ben Hoare, Timothy Hollowood, Joaquin Liniado, James Lucietti, Jose Luis Miramontes, and Daniel Thompson for insightful discussions. The work of PW is supported by the grant ST/X000648/1.
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Cole, L.T., Weck, P. Integrability in gravity from Chern-Simons theory. J. High Energ. Phys. 2024, 80 (2024). https://doi.org/10.1007/JHEP10(2024)080
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DOI: https://doi.org/10.1007/JHEP10(2024)080