Spontaneously Broken Asymptotic Symmetries and an Effective Action for Horizon Dynamics

Abstract

Asymptotic spacetime symmetries have been conjectured to play an important role in quantum gravity. In this paper we study the breaking of asymptotic symmetries associated with a null horizon boundary. In two-dimensions, these symmetries are reparametrizations of the time parameter on the horizon. We show how this horizon reparametrization symmetry is explicitly and spontaneously broken in dilaton gravity and construct an effective action for these pseudo-Goldstone modes using the on-shell gravitational action for a null boundary. The variation of this action yields the horizon constraint equation. This action is invariant under a 2 parameter subgroup of $SL(2)$ transformations, whose Noether charges we interpret via the membrane paradigm. We place these results in the context of recent work on the near $Ad{S}_2$/ near $CF{T}_1$ correspondence. In this setting the horizon action characterizes the infrared regime near the horizon and has a hydrodynamical sigma model form. We also discuss our construction in General Relativity. In the three-dimensional case there is a natural generalization of our results. However, in higher dimensions, the variation of the effective action only yields the Raychaudhuri equation for small perturbations of the horizon.

25 pages, v2: added reference, minor editing

References in corpus (4)

• An Investigation of AdS${}_2$ Backreaction and Holography
• Shaving off Black Hole Soft Hair
• Deconstructing holographic liquids
• On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS Symmetries

Cited by in corpus (5)

• Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• Are non-vacuum states much relevant for retrieving shock wave memory of spacetime?
• Linearized gravity and soft graviton theorem in de Sitter spacetime
• Shock wave quantum memory in shocked detector
• BMS Goldstone modes near the horizon of a Kerr black hole are thermal