Revisiting holographic superconductors with hyperscaling violation

TL;DR

This paper explores how hyperscaling violation influences holographic superconductors, revealing contrasting effects on critical temperature in s-wave and p-wave models and showing it impacts conductivity and gap frequency relations.

Contribution

It provides a detailed analysis of hyperscaling violation effects on both s-wave and p-wave holographic superconductors, including analytical and numerical results that extend previous studies.

Findings

Critical temperature in s-wave models first decreases then increases with hyperscaling violation.

In p-wave models, critical temperature decreases as hyperscaling violation increases.

Hyperscaling violation alters the conductivity and gap frequency relations in both models.

Abstract

We investigate the effect of the hyperscaling violation on the holographic superconductors. In the s-wave model, we find that the critical temperature decreases first and then increases as the hyperscaling violation increases, and the mass of the scalar field will not modify the value of the hyperscaling violation which gives the minimum critical temperature. We analytically confirm the numerical results by using the Sturm-Liouville method with the higher order trial function and improve the previous findings in J. High Energy Phys. {\bf 09}, 048 (2013). However, different from the s-wave case, we note that the critical temperature decreases with the increase of the hyperscaling violation in the p-wave model. In addition, we observe that the hyperscaling violation affects the conductivity of the holographic superconductors and changes the expected relation in the gap frequency in both s-wave and p-wave models.