The volume of the quiver vortex moduli space

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence imposes constraints theories. show that is given by a vacuum expectation value suitable cohomological operator (volume operator) supersymmetric theory, where equations are embedded. In exactly evaluated as contour integral using localization. Graph theory useful to construct and derive formula. formula (generalization Jeffrey–Kirwan residue formula) leads Bradlow bounds ( upper vorticity area surface divided intrinsic size vortex). give some examples various discuss properties these Our formulae applied vortex gauged non-linear sigma model with $\mathbb{C} P^N$ target space, which obtained strong coupling limit parent theory. also non-Abelian generalization “Abelianization”