Abstract
We generalize Nakajima-Yoshioka blowup equations to arbitrary gauge group with hypermultiplets in arbitrary representations. Using our blowup equations, we compute the instanton partition functions for 4d mathcal{N} = 2 and 5d mathcal{N} = 1 gauge theories for arbitrary gauge theory with a large class of matter representations, without knowing explicit construction of the instanton moduli space. Our examples include exceptional gauge theories with fundamentals, SO(N ) gauge theories with spinors, and SU(6) gauge theories with rank-3 antisymmetric hypers. Remarkably, the instanton partition function is completely determined by the perturbative part.
Highlights
ADHM construction of the moduli space [7] provides a direct way to compute the instanton partition function
We have found that this formula agrees with the instanton counting result using the ADHM construction, modulo possible extra factor Zextra that is sensitive to the string theory embedding of the gauge theory
We have found the blowup equations for the Nekrasov partition function that hold for a large set of 4d and 5d gauge theories
Summary
This will allow us to write a recursion relation for the instanton partition function that can be solved rather [5, 20, 21, 28]
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