Towards holographic duals for anomalous supercurrents

In this paper, based on the usual techniques of Gauge/gravity duality, we derive the Ginzburg-Landau current for $s$- wave superconductors in the presence of higher derivative corrections to the abelian gauge sector in the bulk. It has been observed that at sufficiently low temperatures the $U(1)$ current thus computed at the boundary varies inversely with the sixth power of the temperature ($T$) which therefore gives rise to the phenomenon like anomalous superconductivity for the boundary theory. Interestingly we note that this anomalous effect is associated with the leading order higher derivative corrections to the $U(1)$ sector in the bulk.