On the Jeffrey-Kirwan residue of BCD-instantons

Abstract

We apply the Jeffrey-Kirwan method to compute the multiple integrals for the $BCD$ type Nekrasov partition functions of four dimensional $\mathcal{N}=2$ 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 $Z_k^{Sp(0)}=(-1{)}^k(2^{k}k!{\epsilon }_1^k{\epsilon }_2^k{)}^{-1}$ for $k\le 8$, which resembles the formula $Z_k^{U(1)}=(k!{\epsilon }_1^k{\epsilon }_2^k{)}^{-1}$ for the pure super-Yang-Mills theory with gauge group $U(1)$.

arXiv comment23 pages + appendices

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