Holography from Singular Supertranslations on a Black Hole Horizon

TL;DR

This paper explores the extended symmetry structure of black hole horizons, revealing anomalies in dual supertranslations and proposing a holographic Chern-Simons boundary theory to ensure anomaly cancellation and preserve quantum consistency.

Contribution

It demonstrates the presence of anomalies in dual BMS supertranslation generators and proposes a holographic boundary theory to cancel these anomalies, advancing understanding of black hole horizon symmetries.

Findings

Anomalous central term in Dirac brackets of dual supertranslations.

Holographic Chern-Simons theory can cancel the anomaly.

Implication for boundary theories in quantum gravity.

Abstract

We investigate the standard and dual Bondi-Metzner-Sachs (BMS) supertranslation generators on a black hole horizon and draw some conclusions about black hole physics. Recently, it has been shown that in addition to conventional BMS supertranslation symmetries, there exists an additional infinite set of magnetic asymptotic symmetries, dual BMS supertranslations, again parametrized by a function on the two-sphere. We show that the Dirac bracket between these generators exhibits an anomalous central term when one parameter function exhibits a singularity in the complex stereographical coordinates on the sphere. In order to preserve general coordinate invariance, we demonstrate that this central term can be removed by postulating a holographic gravitational Chern-Simons theory on the horizon. This indicates that for an anomaly-free theory of quantum gravity in the presence of a black hole, one should include a boundary theory on the horizon.