Field Theory Models for a Holographic Superconductor in Two Dimensions

TL;DR

This paper explores two-dimensional holographic superconductor models using boundary conditions and phase analysis, revealing phase relations, critical behaviour, and vortex properties with fractional flux.

Contribution

It introduces a field theory framework for holographic superconductors with Robin boundary conditions, linking phase diagrams and vortex phenomena.

Findings

Analytic relation of high- and low-temperature phases via modular invariance.

Matching of near-critical condensate behaviour with Ginzburg–Landau theory.

Identification of fractional magnetic flux vortices analogous to Little–Parks effect.

Abstract

We investigate field theory models of holographic superconductors in which the condensation of the order parameter is induced by a Robin boundary condition. Assuming large-$c$ factorization, we study the phase diagram of a two-dimensional CFT deformed by a relevant double-trace perturbation. Using modular invariance, we relate the high- and low-temperature phases, reproducing analytically the results for the zero-winding sector of the holographic model. Moreover, we match the near-critical behaviour of the condensate with an effective Ginzburg--Landau field theory description. Another important feature of the holographic superconductor is the presence of vortices that carry fractional magnetic flux. We investigate a field theory toy model with similar properties and interpret it as a fractional Little--Parks effect.