Entropy of Flat Space Cosmologies from Celestial dual

TL;DR

This paper constructs a one-dimensional celestial dual theory for (2+1)D flat gravity near Flat Space Cosmologies, capturing their entropy and symmetry breaking, thus providing a new explicit dual description.

Contribution

It introduces a Schwarzian-type 1D dual theory describing BMS$_3$ symmetry breaking in flat space cosmologies, enabling explicit entropy calculations.

Findings

Successfully reproduces the semiclassical entropy of FSCs

Provides an explicit celestial dual construction in (2+1)D

Demonstrates the role of Goldstone bosons in symmetry breaking

Abstract

We construct a one-dimensional dual theory that effectively describes the sector of the (2+1)D flat gravity phase space near a Flat Space Cosmology (FSC) saddle labeled by definite mass and angular momentum. This Schwarzian type action describes the dynamics of the (Pseudo-) Goldstone Bosons of BMS$_3$ algebra on a circle as the symmetry is spontaneously and anomalously broken. This 1D theory, living on the celestial circle, provides an explicit construction of a celestial dual in (2+1)D. We use it to calculate the semiclassical entropy of Flat Space Cosmologies and find perfect agreement with existing literature.