On the Jeffrey–Kirwan residue of BCD-instantons

m. nadratuzzaman hosen, am hasan ali;

We apply the Jeffrey-Kirwan method to compute the multiple integrals for the BCD-type Nekrasov partition functions of four-dimensional N = 2 supersymmetric gauge theories. We construct a graphical distinction rule to determine which poles are surrounded by their integration cycles. We compute the instanton correction of the “Sp(0)” pure super-Yang–Mills theory and find that Z Sp(0) k= (−1)k/2kk!εk1 εk2 for k ≤ 8, which resembles the formula ZU(1) k = 
k!εk1 εk2 −1 for the pure super-Yang–Mills theory with gauge group U(1).