Supersymmetric BCS

TL;DR

This paper explores relativistic BCS superconductivity within N=1 supersymmetric field theories, revealing a first-order phase transition influenced by scalar contributions and supersymmetry, with unique UV cutoff dependencies.

Contribution

It introduces a supersymmetric BCS model with modified Kahler potential, analyzes its phase diagram, and highlights the impact of supersymmetry on the phase transition and cutoff dependence.

Findings

Superconducting phase transition is first order due to scalar effects.

Critical curves depend logarithmically on the UV cutoff.

Supersymmetry alters the standard BCS cutoff dependence.

Abstract

We implement relativistic BCS superconductivity in N=1 supersymmetric field theories with a U(1)_R symmetry. The simplest model contains two chiral superfields with a Kahler potential modified by quartic terms. We study the phase diagram of the gap as a function of the temperature and the specific heat. The superconducting phase transition turns out to be first order, due to the scalar contribution to the one-loop potential. By virtue of supersymmetry, the critical curves depend logarithmically with the UV cutoff, rather than quadratically as in standard BCS theory. We comment on the difficulties in having fermion condensates when the chemical potential is instead coupled to a baryonic U(1)_B current. We also discuss supersymmetric models of BCS with canonical Kahler potential constructed by "integrating-in" chiral superfields.