On the Nekrasov partition function of gauged Argyres-Douglas theories

We study SU(2) gauge theories coupled to (A(1), D-N) theories with or without a fundamental hypermultiplet. For even N, a formula for the contribution of (A(1), D-N) to the Nekrasov partition function was recently obtained by us with Y. Sugawara and T. Uetoko. In this paper, we generalize it to the case of odd N in the classical limit, under the condition that the relevant couplings and vacuum expectation values of Coulomb branch operators of (A(1), D-N) are all turned off. We apply our formula to the (A(2), A(5)) theory to find that its prepotential is related to that of the SU(2) gauge theory with four fundamental flavors by a simple change of variables.

Automated summary

We study the coupling of (A(1), D-N) theories with or without a fundamental hypermultiplet to SU(2) gauge theories. We obtain a formula for the contribution of (A(1), D-N) to the Nekrasov partition function for even N, and generalize it to the case of odd N in the classical limit. We apply our formula to the (A(2), A(5)) theory and find a simple variable change relation between its prepotential and that of the SU(2) gauge theory with four fundamental flavors.