The Infrared Physics of Bad Theories

TL;DR

This paper analyzes the moduli space of 3d $ ext{N}=4$ $U(N)$ SQCD theories, confirming some dualities and clarifying the IR physics of bad theories, including their vacua and symmetry properties.

Contribution

It provides a detailed algebraic description of the Coulomb branch and clarifies the IR behavior and dualities of bad SQCD theories, extending previous results.

Findings

Bad theories flow to the same fixed points as good theories with free hypermultiplets.

A proposed Seiberg-like duality for certain bad theories is invalidated.

A distinguished vacuum preserves all symmetries and matches the dual theory's IR physics.

Abstract

We study the complete moduli space of vacua of 3d $\mathcal{N}=4$ $U(N)$ SQCD theories with $N_f$ fundamentals, building on the algebraic description of the Coulomb branch, and deduce the low energy physics in any vacuum from the local geometry of the moduli space. We confirm previous claims for good and ugly SQCD theories, and show that bad theories flow to the same interacting fixed points as good theories with additional free twisted hypermultiplets. A Seiberg-like duality proposed for bad theories with $N \le N_f \le 2N-2$ is ruled out: the spaces of vacua of the putative dual theories are different. However such bad theories have a distinguished vacuum, which preserves all the global symmetries, whose infrared physics is that of the proposed dual. We finally explain previous results on sphere partition functions and elucidate the relation between the UV and IR $R$-symmetry in this symmetric vacuum.