Comments on AdS_2 Gravity

TL;DR

This work addresses the holographic description of AdS2 gravity by showing that AdS2 Einstein-Maxwell theory emerges from the dimensional reduction of AdS3 gravity with CSS boundary conditions, and by interpreting near-horizon black hole physics through this lens. It establishes a Virasoro plus U(1) Kac-Moody structure in the 2D theory that mirrors the 3D WCFT-like algebra, and demonstrates how near-horizon boundary modes relate to higher-dimensional phenomena such as superradiance. By comparing two global gluing approaches (one with ergoregion, one without), the authors connect negative-energy boundary modes in AdS2 to physical instabilities in the full geometry or to pure gauge modes, depending on global boundary data. Overall, the paper argues for a WCFT-like dual to AdS2 gravity and clarifies how boundary conditions shape the IR description of near-horizon extremal black holes, with implications for supersymmetric and non-supersymmetric cases.

Abstract

We revisit some properties of AdS$_2$ Einstein-Maxwell gravity with the aim of reconciling apparently conflicting results in prior literature. We show that the two dimensional theory can be obtained as a dimensional reduction of the three dimensional Einstein gravity with the CSS boundary condition. In general, this theory on AdS$_2$ can be viewed as an effective theory of the near horizon geometry of a (near-)extremal black hole. We provide an interpretation of our results in terms of the microscopic description of an extremal black hole.