Emergent gauge fields in holographic superconductors

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 phenomenon, 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.