2d theory for asymptotic dynamics of 4d (self-dual) Einstein gravity

TL;DR

This paper introduces a 2D chiral theory on a celestial sphere that reproduces key IR dynamics of 4D self-dual Einstein gravity, connecting 2D CFT computations with 4D asymptotic symmetries.

Contribution

It presents a novel 2D theory framework that captures IR aspects of 4D self-dual Einstein gravity and reproduces known asymptotic symmetry algebras.

Findings

Reproduces 4D BMS algebra using 2D CFT methods

Derives the form of chiral and anti-chiral stress tensors

Shows the necessity of soft mode dressing for hard particles

Abstract

In this paper, we present a simple chiral 2d theory living on a momentum space celestial sphere whose behaviour exactly produces various IR dynamics of recent resurged interests for 4d (selfdual) Einstein gravity in asymptotically flat spacetimes. We demonstrate how to use simple 2d CFT computations to reproduce 4d BMS algebra and $w_{1+\infty}$ algebra, deduce the form of both chiral and anti-chiral stress tensors and recover the necessity for dressing hard particles asymptotically with soft modes. We further discuss how possible extensions of this 2d theory incorporates further dynamical information of 4d Einstein gravity.