Heun's equation and analytic structure of the Gap in Holographic superconductivity

Abstract

We present the new method to calculate the critical temperature as a function of $\Delta$, conformal dimension of the cooper operator. We find that, in the regime $1/2\leq \Delta <1$ where the AC conductivity does not show a gap, the critical temperature is not well defined. We also got expression of AC conductivity for $\Delta=2$, which agrees with numerical result in the probe approximation.