Phases of five-dimensional supersymmetric gauge theories

TL;DR

This paper explores the phase structure of five-dimensional supersymmetric gauge theories with various gauge groups and matter content, revealing universal phase transition patterns and analyzing Wilson loops, thereby supporting the $\

Contribution

It provides a comprehensive analysis of phase diagrams and Wilson loops in 5D supersymmetric gauge theories at large rank, highlighting universality and new phase transition insights.

Findings

Universal third order phase transitions in theories with fundamental hypermultiplets.

Presence of second and third order transitions in $U(N)$ theories.

Wilson loops analyzed for various representations, supporting the $\

Abstract

Five-dimensional $\mathcal{N}=1$ theories with gauge group $U(N)$, $SU(N)$, $USp(2N)$ and $SO(N)$ are studied at large rank through localization on a large sphere. The phase diagram of theories with fundamental hypermultiplets is universal and characterized by third order phase transitions, with the exception of $U(N)$, that shows both second and third order transitions. The phase diagram of theories with adjoint or (anti-)symmetric hypermultiplets is also determined and found to be universal. Moreover, Wilson loops in fundamental and antisymmetric representations of any rank are analyzed in this limit. Quiver theories are discussed as well. All the results substantiate the $\mathcal{F}$-theorem.