Holographic Complexity in Gauge/String Superconductors

TL;DR

This paper investigates the behavior of holographic complexity in two-dimensional gauge/string superconductors with backreactions, revealing divergence near the phase transition from normal to superconducting states.

Contribution

It introduces a method to compute holographic complexity in 2D superconductors with backreactions and analyzes its divergence at the critical temperature.

Findings

Holographic complexity diverges at the superconducting phase transition.

The study applies a perturbation method to analyze complexity behavior.

Complexity behavior differs between normal and superconducting phases.

Abstract

Following a methodology similar to \cite{Alishahiha:2015rta}, we derive a holographic complexity for two dimensional holographic superconductors (gauge/string superconductors) with backreactions. Applying a perturbation method proposed by Kanno in Ref. \cite{kanno}, we study behaviors of the complexity for a dual quantum system near critical points. We show that when a system moves from the normal phase ($T>T_c$) to the superconductor phase ($T<T_c$), the holographic complexity will be divergent.