On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories

TL;DR

This paper explores the dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories, emphasizing the role of flipping fields and discovering new dualities in 3d theories.

Contribution

It investigates the necessity of flipping fields in 3d reductions and presents two new dual Lagrangians for the 3d T[SU(2)] theory.

Findings

Flipping fields are sometimes not needed in 3d reductions.

Two new dual Lagrangians for 3d T[SU(2)] theory are identified.

The role of decoupled operators and flipping fields in dimensional reduction is clarified.

Abstract

Recently, it was found that certain 4d $\mathcal{N}=1$ Lagrangians experience supersymmetry enhancement at their IR fixed point, thereby giving a Lagrangian description for a plethora of Argyres-Douglas theories. A generic feature of these Lagrangians is that a number of gauge invariant operators decouple (as free fields) along the RG-flow. These decoupled operators can be naturally taken into account from the beginning itself by introducing additional gauge singlets (sometimes called `flipping fields') that couple to the decoupled operators via appropriate superpotential terms. It has also been checked that upon dimensionally reducing to 3d, the $(A_1,A_{2n-1})$ type Lagrangians only produce the expected behavior when flipping fields are included in the Lagrangian. In this paper we further investigate the role of flipping fields and find an example where the expected necessity of including the flipping fields in the dimensionally reduced Lagrangians seems to get violated. In the process we find two new dual Lagrangians for the so called 3d $T[SU(2)]$ theory.