Holographic Description of AdS_2 Black Holes

TL;DR

This paper systematically develops the holographic renormalization for AdS_2 gravity, including a boundary mass term for the gauge field, and relates black hole entropy to a dual CFT ground state.

Contribution

It introduces a consistent holographic renormalization scheme for AdS_2 gravity, including a novel boundary mass term, and connects black hole entropy to dual CFT ground state entropy.

Findings

Derived the energy-momentum tensor and central charge for AdS_2

Verified invariance of boundary terms under gauge transformations

Connected AdS_2 black hole entropy to dual CFT ground state

Abstract

We develop the holographic renormalization of AdS_2 gravity systematically. We find that a bulk Maxwell term necessitates a boundary mass term for the gauge field and verify that this unusual term is invariant under gauge transformations that preserve the boundary conditions. We determine the energy-momentum tensor and the central charge, recovering recent results by Hartman and Strominger. We show that our expressions are consistent with dimensional reduction of the AdS_3 energy-momentum tensor and the Brown--Henneaux central charge. As an application of our results we interpret the entropy of AdS_2 black holes as the ground state entropy of a dual CFT.