Heun’s equation and analytic structure of the gap in holographic superconductivity

We present the new method to calculate the critical temperature as a function of Δ , conformal dimension of the cooper operator. We find that, in the regime 1/2≤Δ <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 Δ =2 , which agrees with numerical result in the probe approximation.