Super Yang-Mills on Branched Covers and Weighted Projective Spaces

In this work we conjecture the Coulomb branch partition function, including flux and instanton contributions, for the N=2 vector multiplet on weighted projective space CP²₍ for equivariant Donaldson-Witten and ``Pestun-like'' theories. More precisely, we claim that this partition function agrees with the one computed on a certain branched cover of CP² upon matching conical deficit angles with corresponding branch indices. Our conjecture is substantiated by checking that similar partition functions on spindles agree with their equivalent on certain branched covers of CP¹. We compute the one-loop determinant on the branched cover of CP² for all flux sectors via dimensional reduction from the N=1 vector multiplet on a branched five-sphere along a free S¹-action. This work paves the way for obtaining partition functions on more generic symplectic toric orbifolds.