Singular Supertranslations and Chern-Simons Theory on the Black Hole Horizon

TL;DR

This paper constructs supertranslation charges on a black hole horizon, reveals anomalies in their algebra, and shows that a Chern-Simons theory can restore the symmetry, indicating a new horizon structure.

Contribution

It introduces a Chern-Simons theory on the black hole horizon to cancel anomalies in supertranslation charge algebra, revealing a new horizon structure.

Findings

Supertranslation charges are constructed on the Schwarzschild horizon.

Anomalies in the charge algebra are identified and canceled.

A Chern-Simons theory on the horizon restores the symmetry algebra.

Abstract

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.