Searching for Fermi Surfaces in Super-QED

TL;DR

This paper investigates simple supersymmetric and non-supersymmetric gauge theories at zero temperature to understand Fermi surface formation, revealing that fermions can contribute to charge density without forming a Fermi surface.

Contribution

It provides the first analysis of Fermi surface presence in supersymmetric gauge theories with finite density, showing fermions may not always form Fermi surfaces despite coupling to chemical potentials.

Findings

Fermions do not develop Fermi surfaces in studied supersymmetric models.

Fermions can contribute to charge density without forming a Fermi surface.

Charge can be stored in scalar condensates even when fermions contribute to density.

Abstract

The exploration of strongly-interacting finite-density states of matter has been a major recent application of gauge-gravity duality. When the theories involved have a known Lagrangian description, they are typically deformations of large $N$ supersymmetric gauge theories, which are unusual from a condensed-matter point of view. In order to better interpret the strong-coupling results from holography, an understanding of the weak-coupling behavior of such gauge theories would be useful for comparison. We take a first step in this direction by studying several simple supersymmetric and non-supersymmetric toy model gauge theories at zero temperature. Our supersymmetric examples are $\mathcal{N}=1$ super-QED and $\mathcal{N}=2$ super-QED, with finite densities of electron number and R-charge respectively. Despite the fact that fermionic fields couple to the chemical potentials we introduce, the structure of the interaction terms is such that in both of the supersymmetric cases the fermions do not develop a Fermi surface. One might suspect that all of the charge in such theories would be stored in the scalar condensates, but we show that this is not necessarily the case by giving an example of a theory without a Fermi surface where the fermions still manage to contribute to the charge density.