# On $\mathrm{SQED}_{3}$ and $\mathrm{SQCD}_{3}$: phase transitions and integrability

## TL;DR

This paper investigates phase transitions in supersymmetric Yang-Mills theories on the three-sphere, analyzing partition functions and Wilson loops, and reveals their connection to integrable models like Calogero-Moser systems.

## Contribution

It extends previous work by demonstrating second order phase transitions in non-Abelian theories and links partition functions to integrable models with different R-charges.

## Key findings

- Second order phase transitions in non-Abelian theories
- Partition functions as eigenfunctions of Calogero-Moser models
- Analysis of Wilson loops and R-charge variations

## Abstract

We study supersymmetric Yang-Mills theories on the three-sphere, with massive matter and Fayet-Iliopoulos parameter, showing second order phase transitions for the non-Abelian theory, extending a previous result for the Abelian theory. We study both partition functions and Wilson loops and also discuss the case of different $R$-charges. Two interpretations of the partition function as eigenfunctions of the $A_{1} $ and free $A_{N-1}$ hyperbolic Calogero-Moser integrable model are given as well.