Quantum phase transition in many-flavor supersymmetric QED$_{3}$

TL;DR

This paper analyzes a three-dimensional supersymmetric QED model with many flavors, revealing an exact partition function linked to integrable systems, and identifies a second-order phase transition with critical behavior in the large N limit.

Contribution

It provides an exact analytical solution for the partition function of supersymmetric QED$_{3}$ with multiple flavors, uncovering a phase transition and its critical properties.

Findings

Exact partition function expressed as a conical (Mehler) function

Identification of a second-order phase transition at large N

Divergence of the two-point correlation function near criticality

Abstract

We study $\mathcal{N}=4$ supersymmetric QED in three dimensions, on a three-sphere, with 2N massive hypermultiplets and a Fayet-Iliopoulos parameter. We identify the exact partition function of the theory with a conical (Mehler) function. This implies a number of analytical formulas, including a recurrence relation and a second-order differential equation, associated with an integrable system. In the large N limit, the theory undergoes a second-order phase transition on a critical line in the parameter space. We discuss the critical behavior and compute the two-point correlation function of a gauge invariant mass operator, which is shown to diverge as one approaches criticality from the subcritical phase. Finally, we comment on the asymptotic 1/N expansion and on mirror symmetry.