Phase transitions in 5D super Yang-Mills theory

In this paper we study a phase structure of 5DN=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=1 $$\end{document} super Yang-Mills theory with massive matter multiplets and SU(N ) gauge group. In particular, we are interested in two cases: theory with Nf massive hypermultiplets in the fundamental representation and theory with one adjoint massive hypermultiplet. If these theories are considered on S5 their partition functions can be localized to matrix integrals, which can be approximated by their values at saddle points in the large-N limit. We solve saddle point equations corresponding to the decompactification limit of both theories. We find that in the case of the fundamental hypermultiplets theory experiences third-order phase transition when coupling is varied. We also show that in the case of one adjoint hypermultiplet theory experiences infinite chain of third-order phase transitions, while interpolating between weak and strong coupling regimes.