Singular supertranslations and Chern-Simons theory on the black hole horizon
Ratindranath Akhoury (Leinweber Center for Theoretical Physics, Randall Laboratory of Physics, Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA); Sangmin Choi (CPHT, CNRS, École Polytechnique, Institut Polytechnique de Paris, F-91128 Palaiseau, France); Malcolm J. Perry (School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom; DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, United Kingdom and Trinity College, Cambridge, CB2 1TQ, United Kingdom)
We construct the standard and dual supertranslation charges on the future horizon of the Schwarzschild black hole, using the first-order formulation of gravity with the Holst action. The Dirac bracket algebra of standard and dual supertranslation charges is shown to exhibit a central term in the presence of singularities in the two-sphere function associated with supertranslation. We show that one can cancel this anomalous term and restore the asymptotic symmetry algebra by introducing a gravitational Chern-Simons theory on the horizon. This demonstrates that consistency of the asymptotic symmetry algebra requires a new structure on the horizon.
