Spontaneously Broken Asymptotic Symmetries and an Effective Action for Horizon Dynamics

TL;DR

This paper investigates the breaking of asymptotic horizon symmetries in gravity, constructs an effective action for horizon modes, and explores their implications for quantum gravity and holography.

Contribution

It introduces a novel effective action for horizon reparametrization modes in dilaton gravity and generalizes the framework to higher dimensions.

Findings

Horizon reparametrization symmetry is explicitly and spontaneously broken in dilaton gravity.

The effective action encodes the horizon constraint equation and relates to the membrane paradigm.

In higher dimensions, the action variation yields the Raychaudhuri equation for small perturbations.

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 $AdS_2$/ near $CFT_1$ 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.