Perturbative Holonomy Potentials and Vacua in Chiral Supersymmetric Gauge Theories

Abstract

We present a Wilsonian framework, globally controlled across the holonomy space, for determining the perturbative data governing the vacua of chiral supersymmetric gauge theories on a circle. This allows lifting the Intriligator--Seiberg classification of semiclassical vacua in 3d $\mathcal{N}=2$ Chern--Simons-matter theories to $\RR^3\times S^1$. The framework is showcased by finding a rich set of vacuum sectors in a simple $\U(1)$ model and by reproducing on flat space the R-twisted reduction (first diagnosed on $S^3\times S^1$) of an $\SU(2)$ Maruyoshi--Song theory to the Gang--Yamazaki theory.