Symmetries, Holography and Quantum Phase Transition in Two-dimensional Dilaton AdS Gravity

TL;DR

This paper revisits the Almheiri-Polchinski 2D dilaton gravity model, analyzing symmetry breaking, mass generation, and dual CFT features, providing insights into black hole entropy and vacuum structure.

Contribution

It offers a covariant framework for understanding symmetry breaking, mass, and vacua in 2D dilaton gravity, linking bulk features to dual conformal theories and entropy.

Findings

Symmetry breaking generates an infrared scale and local Goldstone modes.

A non-zero central charge accounts for black hole entropy.

The zero-temperature vacuum with constant dilaton is energetically favored.

Abstract

We present a revisitation of the Almheiri-Polchinski dilaton gravity model from a two-dimensional (2D) bulk perspective. We describe a peculiar feature of the model, namely the pattern of conformal symmetry breaking using bulk Killing vectors, a covariant definition of mass and the flow between different vacua of the theory. We show that the effect of the symmetry breaking is both the generation of an infrared scale (a mass gap) and to make local the Goldstone modes associated with the asymptotic symmetries of the 2D spacetime. In this way a non vanishing central charge is generated in the dual conformal theory, which accounts for the microscopic entropy of the 2D black hole. The use of covariant mass allows to compare energetically the two different vacua of the theory and to show that at zero temperature the vacuum with a constant dilaton is energetically preferred. We also translate in the bulk language several features of the dual CFT discussed by Maldacena et al. The uplifting of the 2D model to $(d+2)-$dimensional theories exhibiting hyperscaling violation is briefly discussed.