Winding branes and persistent currents

Abstract

A D5 brane winding around a stack of D3 branes can be used as a model of persistent current in a thin superconducting ring, with the number N of D3s corresponding to the number of transverse channels in the ring. We consider, in the large N limit, existence and properties of a gapped superconducting state with a uniform winding number density q. We find that there is a gapped classical solution for any q, no matter how large, but when q is larger than a certain q_m the state is unstable with respect to decay by phase slips. We argue that this decay produces strings via a version of the Hanany-Witten effect (in a non-transverse, non-supersymmetric arrangement of branes). This parallels the requirement of quasiparticle production in a clean (disorder-free) wire in field theory of superconductivity.