Analytic structure of the Gap in Holographic superconducrivity

We analytically calculate physical observables of holographic superconductor including the critical temperature and the condensation as functions of $\rho, \;T,\; \Delta$, which are density, temperature and the scaling dimension of the Cooper pair operator respectively. In two spatial dimension, e.g, the critical temperature has the power law dependence on the coupling, $T_{c}\sim (g\rho)^{1/2}$, which can be much higher than the exponential suppression in the BCS theory, $T_{c}\sim\exp({-C/g })$ for small $g$.