An Analytic Holographic Superconductor

TL;DR

This paper presents an analytic approach to studying a holographic superconductor near its phase transition, providing explicit calculations of correlation functions and critical behavior in the dual field theory.

Contribution

It introduces an analytic method for holographic superconductors using Heun equations, extending to higher spin order parameters and proposing a Lagrangian for spin two cases.

Findings

Analytic expressions for current-current correlators near critical temperature

Calculation of second sound speed close to phase transition

Remarks on critical exponents and potential generalizations

Abstract

We investigate a holographic superconductor that admits an analytic treatment near the phase transition. In the dual 3+1 dimensional field theory, the phase transition occurs when a scalar operator of scaling dimension two gets a vacuum expectation value. We calculate current-current correlation functions along with the speed of second sound near the critical temperature. We also make some remarks about critical exponents. An analytic treatment is possible because an underlying Heun equation describing the zero mode of the phase transition has a polynomial solution. Amusingly, the treatment here may generalize for an order parameter with any integer spin, and we propose a Lagrangian for a spin two holographic superconductor.