Emergent Gauge Fields in Holographic Superconductors

TL;DR

This paper explores the effects of introducing dynamical gauge fields into holographic superconductors, revealing their impact on vortex configurations, phase transitions, and critical magnetic fields, and compares these findings with Ginzburg-Landau theory.

Contribution

It demonstrates how dynamical gauge fields can be incorporated into holographic superconductors and analyzes their effects on vortex energetics and phase behavior.

Findings

Holographic superconductors are of Type II (H_c1 < H_c2).

Dynamical gauge fields significantly influence vortex energetics.

Comparison with Ginzburg-Landau theory highlights generic vortex properties.

Abstract

Holographic superconductors have been studied so far in the absence of dynamical electromagnetic fields, namely in the limit in which they coincide with holographic superfluids. It is possible, however, to introduce dynamical gauge fields if a Neumann-type boundary condition is imposed on the AdS-boundary. In 3+1 dimensions, the dual theory is a 2+1 dimensional CFT whose spectrum contains a massless gauge field, signaling the emergence of a gauge symmetry. We study the impact of a dynamical gauge field in vortex configurations where it is known to significantly affect the energetics and phase transitions. We calculate the critical magnetic fields H_c1 and H_c2, obtaining that holographic superconductors are of Type II (H_c1 < H_c2). We extend the study to 4+1 dimensions where the gauge field does not appear as an emergent phenomena, but can be introduced, by a proper renormalization, as an external dynamical field. We also compare our predictions with those arising from a Ginzburg-Landau theory and identify the generic properties of Abrikosov vortices in holographic models.