Holographic P-wave Superconductors in 1+1 Dimensions

TL;DR

This paper explores (1+1)-dimensional p-wave holographic superconductors using Einstein-Maxwell gravity with a vector field, demonstrating vector hair formation below a critical temperature and analyzing conductivity influenced by magnetic moments.

Contribution

It introduces a holographic model for (1+1)-dimensional p-wave superconductors with a vector field and studies their phase transition and conductivity properties.

Findings

Vector hair forms below critical temperature.

Magnetic moment affects boundary conductivity.

Spontaneous symmetry breaking in dual theory.

Abstract

We study $(1+1)$-dimensional p-wave holographic superconductors described by three dimensional Einstein-Maxwell gravity coupled to a massive complex vector field in the context of $AdS_3/CFT_2$ correspondence. In the probe limit where the backreation of matter fields is neglected, we show that there occurs a formation of a vector hair around the black hole below a certain critical temperature. In the dual strongly coupled $(1+1)$-dimensional boundary theory, this holographically corresponds to the formation of a charged vector condensate spontaneously breaking both the $U(1)$ and $SO(1,1)$ symmetries. We numerically compute the ac conductivity for the superconducting phase of the boundary field theory and find that the presence of a magnetic moment term in the dual bulk theory effects the conductivity in the boundary field theory.