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On the Nekrasov Partition Function of Gauged Argyres-Douglas Theories
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abstract
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.
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A note on rank $\frac{3}{2}$ Liouville irregular block
The paper derives the rank 3/2 irregular conformal block for H1 Argyres-Douglas theory via holomorphic anomaly recursion and a deformed Seiberg-Witten curve, exact in the coupling.
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