On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS Symmetries

TL;DR

This paper explores how BMS symmetries act on isolated horizons, revealing spontaneous symmetry breaking and associated Goldstone modes, with implications for horizon physics and holography.

Contribution

It demonstrates the spontaneous breaking of supertranslation and superrotation symmetries on horizons and identifies the corresponding Goldstone modes in both flat and AdS spacetimes.

Findings

Supertranslations shift horizon momentum and are spontaneously broken.

Goldstone bosons associated with broken symmetries shift horizon angular momentum.

Horizon supertranslation Goldstone mode corresponds to holographic superfluid Goldstone mode.

Abstract

We consider a BMS-type symmetry action on isolated horizons in asymptotically flat spacetimes. From the viewpoint of the non-relativistic field theory on a horizon membrane, supertranslations shift the field theory spatial momentum. The latter is related by a Ward identity to the particle number symmetry current and is spontaneously broken. The corresponding Goldstone boson shifts the horizon angular momentum and can be detected quantum mechanically. Similarly, area preserving superrotations are spontaneously broken on the horizon membrane and we identify the corresponding gapless modes. In asymptotically AdS spacetimes we study the BMS-type symmetry action on the horizon in a holographic superfluid dual. We identify the horizon supertranslation Goldstone boson as the holographic superfluid Goldstone mode.