On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS Symmetries

TL;DR

The work addresses how horizon-based BMS-type symmetries act on isolated horizons and their holographic duals. It demonstrates that horizon supertranslations shift the horizon momentum current in a non-relativistic membrane theory, spontaneously breaking particle-number symmetry and producing a Goldstone mode with potential quantum detectability, while area-preserving horizon superrotations yield additional zero-energy modes. The analysis links classical horizon hair to quantum phenomena and clarifies the role of Ward identities in the membrane context. In AdS, the horizon symmetry breaking maps to the boundary superfluid's Goldstone sector, connecting horizon dynamics to the holographic realization of U(1) symmetry breaking.

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.