Instantons from Blow-up

TL;DR

This paper extends blowup equations to general gauge groups with various matter representations, enabling computation of instanton partition functions without explicit moduli space construction, and shows these functions are determined by perturbative data.

Contribution

It generalizes Nakajima-Yoshioka blowup equations to arbitrary gauge groups and matter content, allowing computation of instanton partition functions in broad settings.

Findings

Instanton partition functions are determined solely by perturbative parts.

The method applies to exceptional, SO(N), and SU(6) gauge theories with diverse matter.

Explicit instanton moduli space constructions are not required.

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 N=2 and 5d 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.