From Exact Results to Gauge Dynamics on ${\mathbb{R}}^3\times S^1$

Abstract

We revisit the vacuum structure of the $\mathcal{N}=1$ Intriligator-Seiberg-Shenker model on ${\mathbb{R}}^3\times S^1$. Guided by the Cardy-like asymptotics of its Romelsberger index, and building on earlier semi-classical results by Poppitz and Ünsal, we argue that previously overlooked non-perturbative effects generate a Higgs-type potential on the classical Coulomb branch of the low-energy effective 3d $\mathcal{N}=2$ theory. In particular, on part of the Coulomb branch we encounter the first instance of a dynamically-generated quintic monopole superpotential.

v3: Major revision with a more cogent presentation and several clarifications added. Mention of a preliminary investigation indicating a potential mismatch between the index perspective and the semi-classical approach in the case of the BCI model removed, as we now deem that investigation too crude. 20 pages, 2 figures