Exploring Seiberg-like N-alities with Eight Supercharges

TL;DR

This paper investigates a class of 3d N=4 quiver gauge theories with unitary and special unitary nodes, revealing multiple IR duals (N-alities), emergent Coulomb branch symmetries, and constructing associated 3d mirrors, advancing understanding of Seiberg-like dualities.

Contribution

It introduces the concept of IR N-ality for 3d N=4 quiver theories, develops a method to generate dual theories via quiver mutations, and provides a recipe for constructing their 3d mirrors.

Findings

Multiple IR duals (N-alities) exist for a broad class of 3d N=4 quiver theories.

Emergent Coulomb branch symmetries can be identified and sometimes match UV symmetries.

A systematic construction of 3d mirrors for N-al sets is provided.

Abstract

We show that a large subclass of 3d $\mathcal{N}=4$ quiver gauge theories consisting of unitary and special unitary gauge nodes with only fundamental/bifundamental matter have multiple Seiberg-like IR duals. A generic quiver $\mathcal{T}$ in this subclass has a non-zero number of balanced special unitary gauge nodes and it is a good theory in the Gaiotto-Witten sense. We refer to this phenomenon as "IR N-ality" and the set of mutually IR dual theories as the "N-al set" associated with the quiver $\mathcal{T}$. Starting from $\mathcal{T}$, we construct a sequence of dualities by step-wise implementing a set of quiver mutations which act locally on the gauge nodes. The associated N-al theories can then be read off from this duality sequence. The quiver $\mathcal{T}$ generically has an emergent Coulomb branch global symmetry in the IR, such that the rank of the IR symmetry is always greater than the rank visible in the UV. We show that there exists at least one theory in the N-al set for which the rank of the IR symmetry precisely matches the rank of the UV symmetry. In certain special cases that we discuss in this work, the correct emergent symmetry algebra itself may be read off from this preferred theory (or theories) in addition to the correct rank. Finally, we give a recipe for constructing the 3d mirror associated with a given N-al set and show how the emergent Coulomb branch symmetry of $\mathcal{T}$ is realized as a UV-manifest Higgs branch symmetry of the 3d mirror. This paper is the second in a series of four papers on 3d $\mathcal{N}=4$ Seiberg-like dualities, preceded by the work [arXiv:2210.04921].