Holographic positive energy theorems in three-dimensional gravity

TL;DR

This work shows that the covariant phase space for three-dimensional gravity, both in asymptotically flat and AdS settings, is governed by Virasoro coadjoint orbits. By analyzing the energy functional on these orbits, the authors derive explicit positive energy conditions: in flat space, the absolute energy minimum is $E_{min}=-\frac{1}{8G}$ attained at a specific constant coadjoint value, while in AdS$_3$ gravity the minimum is set by $M=-1/(8G)$ with $J=0$, with precise bounds on mass and angular momentum. The approach relies on Schwarzian inequalities and the detailed orbit structure to determine which geometries are allowed, linking holographic reductions to the positivity of energy. The results highlight the delicate role of zero modes, holonomies, and the coupling of chiral sectors in the AdS case, and point to several open directions, including a full BMS$_3$ orbit classification and extensions to higher dimensions.

Abstract

The covariant phase space of three-dimensional asymptotically flat and anti-de Sitter gravity is controlled by well-understood coadjoint orbits of the Virasoro group. Detailed knowledge on the behavior of the energy functional on these orbits can be used to discuss positive energy theorems.