The dual Ginzburg-Landau theory for a holographic superconductor: Finite coupling corrections

TL;DR

This paper derives the dual Ginzburg-Landau theory for a finite coupling holographic superconductor, revealing that the system becomes more Type-II-like and addressing previous issues in the theoretical framework.

Contribution

It extends the dual GL theory to finite coupling in holographic superconductors, providing exact numerical coefficients and correcting prior assumptions.

Findings

The GL parameter $$ increases at finite coupling, indicating a shift towards Type-II superconductivity.

The condensate increases at finite coupling, contrary to previous beliefs.

Identification of potential issues in the naive AdS/CFT dictionary and condensate determination.

Abstract

The holographic superconductor is the holographic dual of superconductors. We recently identified the dual Ginzburg-Landau (GL) theory for a class of bulk 5-dimensional holographic superconductors (arXiv:2207.07182 [hep-th]). However, the result is the strong coupling limit or the large-$N_c$ limit. A natural question is how the dual GL theory changes at finite coupling. We identify the dual GL theory for a minimal holographic superconductor at finite coupling (Gauss-Bonnet holographic superconductor), where numerical coefficients are obtained exactly. The GL parameter $\kappa$ increases at finite coupling, namely the system approaches a more Type-II superconductor like material. We also point out two potential problems in previous works: (1) the "naive" AdS/CFT dictionary, and (2) the condensate determined only from the GL potential terms. As a result, the condensate increases at finite coupling unlike common folklore.