$\widehat{sl_2}$ symmetry of ${\mathbb R}^{1,3}$ gravity

TL;DR

This paper introduces new boundary conditions for four-dimensional Einstein gravity that reveal an extended asymptotic symmetry algebra, including Virasoro and current algebras, linking bulk symmetries to celestial CFT structures.

Contribution

It proposes novel asymptotic boundary conditions for 4D Einstein gravity that uncover an extended symmetry algebra involving Virasoro and current algebras, connecting bulk and celestial CFT symmetries.

Findings

Asymptotic symmetries form a Virasoro and current algebra extension of Poincare.

Boundary conditions are consistent with the variational principle.

Symmetries relate to celestial CFT correlation functions.

Abstract

We propose novel asymptotically locally flat boundary conditions for Einstein Gravity without cosmological constant in four dimensions that are consistent with the variational principle. They allow for complex solutions that are asymptotically diffeomorphic to flat space-times under complexified diffeomorphisms. We show that the resultant asymptotic symmetries are an extension of the Poincare algebra to a copy of Virasoro, a chiral $\mathfrak{sl}(2,{\mathbb C})$ current algebra along with two chiral $\mathfrak{u}(1)$ currents. We posit that these bulk symmetries are direct analogues of the recently discovered chiral algebra symmetries of gravitational scattering amplitudes as celestial CFT correlation functions.