Phase transitions and Wilson loops in antisymmetric representations in Chern-Simons-matter theory

TL;DR

This paper analyzes phase transitions and Wilson loop behaviors in 3D $ ext{U}(N)$ Chern-Simons-matter theory with massive hypermultiplets, revealing how different phases and representation sizes affect the theory's properties.

Contribution

It extends saddle-point solutions to asymmetric intervals and explores Wilson loops in antisymmetric representations with FI terms, providing explicit formulas and phase transition analysis.

Findings

Identification of phase diagrams in the decompactification limit.

Explicit expressions for Wilson loops with and without FI terms.

Demonstration of phase transition orders and their mechanisms.

Abstract

We study the phase transitions of three-dimensional $\mathcal{N}=2$ $U(N)$ Chern-Simons theory on $\mathbb{S}^3$ with a varied number of massive fundamental hypermultiplets and with a Fayet-Iliopoulos parameter. We characterize the various phase diagrams in the decompactification limit, according to the number of different mass scales in the theory. For this, we extend the known solution of the saddle-point equations to the setting where the one cut solution is characterized by asymmetric intervals. We then study the large $N$ limit of Wilson loops in antisymmetric representations, with the additional scaling corresponding to the variation of the size of the representation. We give explicit expressions, both with and without FI terms, and study $1/R$ corrections for the different phases. These corrections break the perimeter law behavior, as they introduce a scaling with the size of the representation. We show how the phase transitions of the Wilson loops can either be of first or second order and determine the underlying mechanism in terms of the eventual asymmetry of the support of the solution of the saddle-point equation, at the critical points.