Low temperature properties of holographic condensates

Abstract

In the current work we study various models of holographic superconductors at low temperature. Generically the zero temperature limit of those models are solitonic solution with a zero sized horizon. Here we generalized simple version of those zero temperature solutions to small but non-zero temperature T. We confine ourselves to cases where near horizon geometry is AdS 4. At a non-zero temperature a small horizon would form deep inside this AdS 4 which does not disturb the UV physics. The resulting geometry may be matched with the zero temperature solution at an intermediate length scale. We understand this matching from separation of scales by setting up a perturbative expansion in gauge potential. We have a better analytic control in abelian case and quantities may be expressed in terms of hypergeometric function. From this we calculate low temperature behavior of various quatities like entropy, charge density and specific heat etc. We also calculate various energy gaps associated with p-wave holographic superconductor to understand the underlying pairing mechanism. The result deviates significantly from the corresponding weak coupling BCS counterpart.