Vortices , wall-crossing and 3d Seiberg like dualities

We explore 1d vortex dynamics of 3d supersymmetric Yang-Mills theories, as inferred from factorization of exact
partition functions. Under Seiberg-like dualities, the 3d partition function must remain invariant, yet it is not a
priori clear what should happen to the vortex dynamics. We observe that the 1d quivers for the vortices remain the
same, and the net effect of the 3d duality map manifests as 1d Wall-Crossing phenomenon; Although the vortex
number can shift along such duality maps, the ranks of the 1d quiver theory are unaffected, leading to a notion of
fundamental vortices as basic building blocks for topological sectors. For Aharony-type duality, in particular,
where one must supply extra chiral fields to couple with monopole operators on the dual side, 1d wall-crossings
of an infinite number of vortex quiver theories are neatly and collectively encoded by 3d determinant of such
extra chiral fields.