Exact partition function in $U(2)\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms

Abstract

We exactly compute the partition function for $U(2)_k\times U(2)_{-k}$ ABJM theory on $\mathbb S^3$ deformed by mass $m$ and Fayet-Iliopoulos parameter $\zeta $. For $k=1,2$, the partition function has an infinite number of Lee-Yang zeros. For general $k$, in the decompactification limit the theory exhibits a quantum (first-order) phase transition at $m=2\zeta $.