Noncommutative $p$-wave holographic superconductors

Abstract

In this work, we have studied the effects of noncommutative geometry on the properties of p-wave holographic superconductors with massive vector condensates in the probe limit. We have applied the St\"{u}rm-Liouville eigenvalue approach to analyse the model. In this model, we have calculated the critical temperature and the value of the condensation operator for two different values of $m^2$. We have also shown how the influence of noncommutative geometry modifies these quantities. Finally, by applying a linearised gauge field perturbation along the boundary direction, we calculated the holographic superconductor's AC conductivity using a self-consistent approach and then carried out a more rigorous analysis. The noncommutative effects are also found to be present in the result of AC conductivity. We have also found that just like the commutative case, here the DC conductivity diverges due to the presence of a first order pole in the frequency regime.