Asymptotic symmetries of AdS_2 and conformal group in d=1

TL;DR

Problem: how to realize AdS2 asymptotic symmetries and their CFT1 dual in 2D dilaton gravity. Approach: promote SL(2,R) isometries to a Virasoro-like boundary algebra, compute its central extension in a canonical framework, and count boundary microstates via Cardy. Key results: the asymptotic symmetry algebra on AdS2 yields a Virasoro algebra with central charge c=24η0; microscopic entropy from Cardy agrees with the JT thermodynamic entropy up to a factor √2 and extends to general 2D dilaton gravities with asymptotically AdS behavior. Significance: provides a concrete holographic account of 2D black hole entropy, clarifies the AdS2/CFT1 structure, and highlights the roles of topology and the dilaton in holography.

Abstract

We present a detailed discussion of the asymptotic symmetries of Anti-de Sitter space in two dimensions and their relationship with the conformal group in one dimension. We use this relationship to give a microscopical derivation of the entropy of 2d black holes that have asymptotically Anti-de Sitter behaviour. The implications of our results for the conjectured AdS_2/CFT_1 duality are also discussed.