Holographic Symmetry-Breaking Phases in AdS$_3$/CFT$_2$

TL;DR

This paper investigates symmetry-breaking phases in 3D gravity coupled to matter, revealing metastable phases with broken symmetry in discrete cases and continuous symmetry breaking at low temperatures, with implications for AdS/CFT correspondence.

Contribution

It provides a detailed analysis of symmetry-breaking phases in 3D gravity models, including black holes with scalar hair and Einstein-Maxwell theory, highlighting novel metastable and continuous symmetry-breaking phenomena.

Findings

Metastable phases of broken symmetry in discrete cases.

Continuous symmetry breaking at low temperatures.

Discussion on compatibility with Coleman-Mermin-Wagner theorem.

Abstract

In this note we study the symmetry-breaking phases of 3D gravity coupled to matter. In particular, we consider black holes with scalar hair as a model of symmetry-breaking phases of a strongly coupled 1+1 dimensional CFT. In the case of a discrete symmetry, we show that these theories admit metastable phases of broken symmetry and study the thermodynamics of these phases. We also demonstrate that the 3D Einstein-Maxwell theory shows continuous symmetry breaking at low temperature. The apparent contradiction with the Coleman-Mermin-Wagner theorem is discussed.