Holographic phase transitions from higgsed, non abelian charged black holes

TL;DR

This paper explores holographic phase transitions in a gravity-Yang-Mills-Higgs framework, revealing how gauge symmetry breaking influences superconducting phases and identifying critical couplings affecting transition order and existence of solutions.

Contribution

It introduces new solutions for charged black holes with symmetry breaking and analyzes phase transition orders and ground states in holographic superconductor models.

Findings

Second order transitions for p+ip superconductors.

First order transitions occur for p-wave superconductors beyond a critical gravitational coupling.

Ground state solutions are domain walls interpolating between different AdS_4 geometries.

Abstract

We find solutions of a gravity-Yang-Mills-Higgs theory in four dimensions that represent asymptotic anti-de Sitter charged black holes with partial/full gauge symmetry breaking. We then apply the AdS/CFT correspondence to study the strong coupling regime of a $2+1$ quantum field theory at temperature $T$ and finite chemical potential, which undergoes transitions to phases exhibiting the condensation of a composite charged vector operator below a critical temperature $T_c$, presumably describing $p+ip/p$-wave superconductors. In the case of $p+ip$-wave superconductors the transitions are always of second order. But for $p$-wave superconductors we determine the existence of a critical value $\alpha_c$ of the gravitational coupling (for fixed Higgs v.e.v. parameter $\hat m_W$) beyond which the transitions become of first order. As a by-product, we show that the $p$-wave phase is energetically favored over the $p+ip$ one, for any values of the parameters. We also find the ground state solutions corresponding to zero temperature. Such states are described by domain wall geometries that interpolate between $AdS_4$ spaces with different light velocities, and for a given $\hat m_{W}$, they exist below a critical value of the coupling. The behavior of the order parameter as function of the gravitational coupling near the critical coupling suggests the presence of second order quantum phase transitions. We finally study the dependence of the solution on the Higgs coupling, and find the existence of a critical value beyond which no condensed solution is present.