Building (1+1) holographic superconductors in the presence of non-linear Electrodynamics

TL;DR

This paper investigates (1+1)-dimensional holographic superconductors within the gauge/gravity duality framework, analyzing the effects of non-linear electrodynamics on critical temperature using analytical methods.

Contribution

It introduces an analytical study of (1+1)-dimensional holographic superconductors with non-linear electrodynamics in the gravity dual, extending previous models to include Einstein-power-Maxwell fields.

Findings

Critical temperature depends on scalar mass and non-linear electrodynamics parameters.

Analytical expressions for transition temperature are derived.

Comparison with higher-dimensional models highlights unique features of (1+1)-dimensional superconductors.

Abstract

In the framework of the gauge/gravity duality, and in particular of the $AdS_3/CFT_2$ correspondence, we study one-dimensional superconductors analyzing the dual (1+2)-dimensional gravity in the presence of the Einstein-power-Maxwell non-linear Electrodynamics. In the probe limit we compute the critical temperature of the transition as a function of the mass of the scalar field. The computation is performed analytically employing the Rayleigh-Ritz variational principle. The comparison with a power Maxwell field in higher dimensions as well as with the (1+3)-dimensional Einstein-Maxwell theory for two-dimensional superconductors is made as well.