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

Makoto Natsuume

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 $κ$ 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.

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

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- 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 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.
Paper Structure (33 sections, 181 equations, 1 figure)

This paper contains 33 sections, 181 equations, 1 figure.

Table of Contents

  1. Introduction and Summary
  2. Two problems in previous works
  3. Preliminaries
  4. The GB black hole
  5. The choice of $N_\text{\tiny{GB}}$:
  6. The sign of $\lambda_\text{\tiny{GB}}$:
  7. A caution:
  8. The holographic superconductor
  9. The asymptotic behavior:
  10. Technical differences from Ref. Gregory:2009fj:
  11. Counterterms:
  12. Qualitative analysis
  13. The critical point
  14. High-temperature phase
  15. The order parameter response function:
  16. ...and 18 more sections

Figures (1)

  • Figure 1: The canonically normalized condensate $|\phi|$. The dashed (blue) line represents the strong coupling limit. The solid green and orange lines represent the condensate at finite coupling ($\lambda_\text{\tiny{GB}}=0.1$) using the naive dictionary and our dictionary, respectively.