Three Roads to Probe-Brane Superconductivity

TL;DR

This paper investigates different mechanisms for superconductivity in a holographic defect system using probe branes, revealing the internal scalar as the most thermodynamically favored phase with complex phase transition behaviors.

Contribution

It compares three superconducting phases in a holographic setup and introduces a simplified DBI action that clarifies phase transition orders and resolves divergences.

Findings

Internal scalar has the highest critical temperature.

Some second order transitions become first order in the simplified model.

Ground state degeneracy is lifted in the preferred phase.

Abstract

We study a defect system of two parallel D5 probe branes in a large-N_c D3 background. Using the non-abelian DBI action, we study three different fields that can give rise to a superconducting phase transition: A vector (p-wave), a scalar corresponding to a non-trivial "separation"' of the branes in the (3+1) field theory directions and a scalar corresponding to a separation in the "internal" S^5 (both s-wave). Comparing these phases first in the \alpha'^2 expansion, we find that the internal scalar has the largest critical temperature and is always thermodynamically preferred. Further, there is an interesting attractor behavior. Taking a simplified version of the full DBI action that preserves its regularity and geometry, we find that the divergences of the \alpha'^2 expansion are resolved and some second order transitions turn into first order ones. In addition to some other changes of the phase diagram due to the structure of the DBI action, we observe that the ground state degeneracy of the unbroken theory is lifted. We also isolate the unphysical artifacts of our simplification.