Supertranslations and Holography near the Horizon of Schwarzschild Black Holes

TL;DR

The paper analyzes horizon-boundary symmetries of Schwarzschild black holes, showing horizon supertranslations form an infinite commuting algebra mirroring BMS at null infinity. It then develops a holographic picture where a three-dimensional boundary theory on the near-horizon cone becomes conformal and gapless at a quantum critical point in the large-N limit, with horizon Bogoliubov modes acting as Goldstone bosons. In the quantum regime (finite N), these modes acquire a small mass and nonzero charges, leading to a finite entropy and a nondegenerate, quantum-resolved bulk metric. The work thus connects horizon symmetries to a holographic, quantum-critical description of black hole microstates and highlights how quantum corrections resolve classical degeneracies of the horizon.

Abstract

In this paper we review and discuss several aspects of supertranslations and their associated algebras at the horizon of a Schwarzschild black hole. We will compare two different approaches on horizon supertranslations, which were recently considered in separate publications. Furthermore we describe a possible holographic description of a Schwarzschild black hole in terms of a large N boundary theory, which accommodates the Goldstone bosons of the horizon supertranslations.