What is the dual Ginzburg-Landau theory for holographic superconductors?

TL;DR

This work identifies the dual Ginzburg–Landau theory for holographic superconductors by performing analytic bulk calculations at the BF-bound critical point in a 5D setup and enforcing a holographic semiclassical boundary condition to render the Maxwell field dynamical. By matching bulk response functions and the homogeneous condensate to GL quantities, the authors determine explicit GL coefficients and show that B_{c2} = −1/ξ_>^2 holds exactly in this holographic context, with the GL parameter κ determined by μ_m and the bulk couplings. The analysis extends from minimal to nonminimal holographic superconductors, revealing how bulk parameters A and B modify the quartic coupling and thereby affect κ, B_c, and the vortex lattice energetics (favoring a triangular Abrikosov lattice). Overall, the paper provides a first-principles, analytic bridge between holographic superconductors and GL theory, clarifying Meissner physics in holography and offering a framework to explore strong-coupling superconductivity beyond conventional GL descriptions.

Abstract

Holographic superconductors are holographic duals of superconductors. Macroscopically, a superconductor should be described by the Ginzburg-Landau (GL) theory. There is ample evidence that the holographic superconductors are described by the standard GL theory, but the exact form of the dual GL theory is little known. We identify the dual GL theory for a class of bulk 5-dimensional holographic superconductors, where numerical coefficients are obtained exactly.