We show that a large subclass of 3d 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 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 T. Starting
from 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 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 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 N=4 Seiberg-like dualities,
preceded by the work [arXiv:2210.04921].Comment: v1:48 pages + references. Quiver diagrams are color-coded, v2:
References updated, v3: An error corrected in figure 2 and figure 10, section
2.3 on quiver mutations expanded for better presentation, minor typos fixed,
v4: An important typo fixe