Relations between supersymmetric structures in UV and IR for $\mathcal{N}=4$ bad theories

TL;DR

This paper explores the possible infrared fixed point structures of three-dimensional $ =4$ bad theories, revealing various scenarios for UV-IR symmetry relations and providing examples, including an SU(2) SYM case.

Contribution

It systematically analyzes the IR fixed points of $ =4$ bad theories, proposing multiple possible structures and relations between UV and IR symmetries, with concrete examples.

Findings

Multiple IR fixed point structures are possible for $ =4$ bad theories.

The SU(2) SYM with two hypermultiplets flows to an interacting SCFT.

Open question on whether all proposed options are realized.

Abstract

We investigate options for the structure of the infrared fixed points of $\mathcal{N}=4$ bad theories in three dimensions. Unitarity constraints allow a number of possibilities, not necessarily a product of an interacting $\mathcal{N}=4$ SCFT and free theories. For each option we provide relations between the UV and IR $R-$symmetry groups. For some of them we give examples. In particular, the $\mathcal{N}4$ SU(2) SYM with two fundamental hypermultiplets is an example of a bad theory which flows to an interacting irreducible SCFT in the IR. The question of whether all the options are realized remains open.