Low-temperature behavior of the Abelian Higgs model in anti-de Sitter space

TL;DR

This paper investigates the low-temperature phases of the Abelian Higgs model in AdS_4, revealing a second order phase transition, superconducting black holes, and domain wall structures with specific optical properties.

Contribution

It extends previous studies by including back-reaction effects and analyzing the emergence of domain walls and conductivity in the low-temperature regime.

Findings

Second order phase transition at finite temperature

Superconducting black hole solutions observed

Emergence of domain wall structures at low temperatures

Abstract

We explore the low-temperature behavior of the Abelian Higgs model in AdS_4, away from the probe limit in which back-reaction of matter fields on the metric can be neglected. Over a significant range of charges for the complex scalar, we observe a second order phase transition at finite temperature. The symmetry-breaking states are superconducting black holes. At least when the charge of the scalar is not too small, we observe at low temperatures the emergence of a domain wall structure characterized by a definite index of refraction. We also compute the conductivity as a function of frequency.