Holographic Complexity in Gauge/String Superconductors

TL;DR

The paper investigates holographic complexity in a 2D gauge/string superconductor within the AdS$_3$/CFT$_2$ framework, incorporating backreaction beyond the probe limit. A domain-wall RG-inspired approach and a perturbative expansion in the coherence length are used to compute the bulk volume that defines complexity, accounting for backreaction on the BTZ black hole background. It shows that holographic complexity diverges as the system crosses the normal-to-superconductor transition, with the leading behavior tied to approaching the critical chemical potential $\mu_c$ (and temperature $T_c$). These results link holographic complexity to fidelity-susceptibility–like signals of quantum phase transitions and highlight backreaction as a key factor shaping critical behavior in holographic superconductors.

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.