# Properties of the partition function of ${\cal N}=2$ supersymmetric QCD with massive matter

## TL;DR

This paper investigates the phase structure of massive ${
m extbf{N}=2}$ supersymmetric QCD with gauge groups $SU(2)$ and $SU(3)$, revealing a transition between weak and strong coupling phases characterized by saddle-point analysis and superconformal sectors.

## Contribution

It provides an exact analysis of phase transitions in ${
m extbf{N}=2}$ SQCD using supersymmetric localization and Seiberg-Witten theory, identifying critical points and phase behavior.

## Key findings

- Two distinct phases identified: weak and strong coupling.
- Phase transition appears second-order with divergent susceptibility.
- Critical points involve superconformal field theories or sectors.

## Abstract

We study the different quantum phases that occur in massive ${\cal N}=2$ supersymmetric QCD with gauge groups $SU(2)$ and $SU(3)$ as the coupling $\Lambda/M$ is gradually increased from 0 to infinity. The phases can be identified by computing the exact partition function by saddle-points, combining supersymmetric localization and the Seiberg-Witten formalism. In all cases, we find two phases, a weak coupling and a strong coupling phase, separated by a critical point described by a superconformal field theory or involving superconformal sectors. In crossing the critical point, the dominant saddle-point hops from one singularity of the curve to another one. The theories seem to undergo a second-order phase transition with divergent susceptibility.