Low-temperature behavior of the Abelian Higgs model in anti-de Sitter space
Abstract
We explore the low-temperature behavior of the Abelian Higgs model in AdS4, 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.
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