Super Yang-Mills on branched covers and weighted projective spaces

Abstract

Abstract In this work we conjecture the Coulomb branch partition function, including flux and instanton contributions, for the N $$ \mathcal{N} $$ = 2 vector multiplet on weighted projective space CP N 2 $$ {\mathbbm{CP}}_N^2 $$ 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 CP 2 $$ {\mathbbm{CP}}^2 $$ 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 CP 1 $$ {\mathbbm{CP}}^1 $$ . We compute the one-loop determinant on the branched cover of CP 2 $$ {\mathbbm{CP}}^2 $$ for all flux sectors via dimensional reduction from the N $$ \mathcal{N} $$ = 1 vector multiplet on a branched five-sphere along a free S 1-action. This work paves the way for obtaining partition functions on more generic symplectic toric orbifolds.

Keywords

• Nonperturbative Effects
• Supersymmetric Gauge Theory
• Extended Supersymmetry