JT gravity from holographic reduction of 3D asymptotically flat spacetime

TL;DR

This paper demonstrates how 3D flat spacetime gravity can be reduced holographically to a 1D Schwarzian theory via JT gravity, revealing a novel connection between superrotation modes and boundary reparametrizations.

Contribution

It introduces a holographic reduction from 3D flat spacetime to JT gravity and derives a dual Schwarzian theory, linking superrotation modes to boundary reparametrizations.

Findings

JT gravity emerges on fluctuating branes in flat spacetime

The dual 1D Schwarzian theory encodes superrotation modes

Holographic reduction connects 3D flat spacetime to 2D and 1D theories

Abstract

We attempt to understand the CFT$_1$ structure underlying (2+1)D gravity in flat spacetime via dimensional reduction. We observe that under superrotation, the hyperbolic (and dS$_2$) slices of flat spacetime transform to asymptotically (A)dS$_2$ slices. We consider a wedge region bounded by two such surfaces as End-of-the-World branes and employ Wedge holography to perform holographic reduction. We show that once we consider fluctuating branes, the localised theory on the branes is Jackiw-Teitelboim (JT) theory. Finally, using the dual description of JT, we derive an 1D Schwarzian theory at the spatial slice of null infinity. In this dual Celestial (nearly) CFT, the superrotation mode of 3D plays the role of the Schwarzian derivative of the boundary time reparametrization mode.