Instantons from blow-up

Abstract

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 $$ \mathcal{N} $$ N = 2 and 5d $$ \mathcal{N} $$ 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.