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

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.

15 pages, 7 figure

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• Conductivity of the one-dimensional holographic p-wave superconductors in the presence of nonlinear electrodynamics
• Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields
• Analytical approach to phase transitions in rotating and non-rotating 2D holographic superconductors
• Fermions in an AdS3 Black Hole Background and the Gauge-Gravity Duality