The Effective Action of Superrotation Modes

TL;DR

This paper derives an effective two-dimensional conformal action governing superrotation modes in four-dimensional asymptotically flat gravity, revealing symmetry breaking phenomena on the celestial sphere.

Contribution

It introduces a novel Alekseev--Shatashvili action for superrotation modes derived from a Chern--Simons formulation of asymptotic gravity.

Findings

Superrotation modes are described by an Alekseev--Shatashvili action.

The theory captures spontaneous and explicit symmetry breaking of Virasoro and Diff$( ext{S}^2)$ superrotations.

Reformulation of asymptotic field equations in a Chern--Simons framework.

Abstract

Starting from an analysis of four-dimensional asymptotically flat gravity in first order formulation, we show that superrotation reparametrization modes are governed by an Alekseev--Shatashvili action on the celestial sphere. This two-dimensional conformal theory describes spontaneous symmetry breaking of Virasoro superrotations together with the explicit symmetry breaking of more general Diff$(\mathcal{S}^2)$ superrotations. We arrive at this result by first reformulating the asymptotic field equations and symmetries of the radiative vacuum sector in terms of a Chern--Simons theory at null infinity, and subsequently performing a Hamiltonian reduction of this theory onto the celestial sphere.