On ${\mathrm{SQED}}_3$ and ${\mathrm{SQCD}}_3$: phase transitions and integrability

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.

11 pages, 5 figures