FI-flows of 3d N=4 Theories

TL;DR

This paper introduces a new quiver algorithm to analyze RG-flows in 3d N=4 theories triggered by Fayet-Iliopoulos deformations, providing systematic insights into mass deformations and revealing new mirror pairs.

Contribution

It presents a novel quiver algorithm connecting linear algebra and graph theory to study RG-flows in 3d N=4 theories, with applications to SQCD and 4d N=2 SCFTs.

Findings

Systematic exploration of RG-flows via magnetic quivers.

Discovery of a new 3d mirror pair.

Application to SQCD and 4d N=2 SCFTs.

Abstract

We study the 3d $\mathcal{N}=4$ RG-flows triggered by Fayet-Iliopoulos deformations in unitary quiver theories. These deformations can be implemented by a new quiver algorithm which contains at its heart a problem at the intersection of linear algebra and graph theory. When interpreted as magnetic quivers for SQFTs in various dimensions, our results provide a systematic way to explore RG-flows triggered by mass deformations and generalizations thereof. This is illustrated by case studies of SQCD theories and low rank 4d $\mathcal{N}=2$ SCFTs. A delightful by-product of our work is the discovery of an interesting new 3d mirror pair.