Ground states of holographic superconductors

TL;DR

This paper explores the ground states of holographic superconductors modeled by the Abelian Higgs model in AdS_4, revealing conditions for emergent conformal or Lifshitz-like infrared symmetries based on scalar charge and potential.

Contribution

It provides a detailed analysis of how different scalar potentials and parameters influence the infrared behavior of holographic superconductor ground states, including emergent symmetries.

Findings

Large scalar charge leads to emergent conformal symmetry in the IR.

Small scalar charge results in Lifshitz-like IR scaling.

Lifshitz-like scaling is the only IR behavior for positive mass quadratic potentials.

Abstract

We investigate the ground states of the Abelian Higgs model in AdS_4 with various choices of parameters, and with no deformations in the ultraviolet other than a chemical potential for the electric charge under the Abelian gauge field. For W-shaped potentials with symmetry-breaking minima, an analysis of infrared asymptotics suggests that the ground state has emergent conformal symmetry in the infrared when the charge of the complex scalar is large enough. But when this charge is too small, the likeliest ground state has Lifshitz-like scaling in the infrared. For positive mass quadratic potentials, Lifshitz-like scaling is the only possible infrared behavior for constant nonzero values of the scalar. The approach to Lifshitz-like scaling is shown in many cases to be oscillatory.