AdS_2 Gravity as Conformally Invariant Mechanical System

TL;DR

This paper demonstrates that 2D AdS gravity induces a conformally invariant boundary dynamics describable by a de Alfaro-Fubini-Furlan model, linking boundary symmetries to black hole entropy.

Contribution

It establishes a novel boundary description of 2D AdS gravity as a conformally invariant mechanical system with a Virasoro algebra symmetry.

Findings

Derived the boundary conformal dynamics from 2D AdS gravity.

Calculated the Virasoro algebra's central charge.

Matched statistical and thermodynamical entropy of AdS_2 black holes.

Abstract

We show that two-dimensional (2D) AdS gravity induces on the spacetime boundary a conformally invariant dynamics that can be described in terms of a de Alfaro-Fubini-Furlan model coupled to an external source with conformal dimension two. The external source encodes the information about the gauge symmetries of the 2D gravity system. Alternatively, there exists a description in terms of a mechanical system with anholonomic constraints. The considered systems are invariant under the action of the conformal group generated by a Virasoro algebra, which occurs also as asymptotic symmetry algebra of two-dimensional anti-de Sitter space. We calculate the central charge of the algebra and find perfect agreement between statistical and thermodynamical entropy of AdS_2 black holes.