6d strings and exceptional instantons

TL;DR

This paper introduces new ADHM-like methods to compute instanton partition functions and elliptic genera for 5d and 6d supersymmetric gauge theories with exceptional gauge groups and matters, supported by various tests and D-brane approaches.

Contribution

It develops novel ADHM-like techniques for exceptional gauge groups and studies their instanton and string spectra, expanding computational tools in supersymmetric gauge theories.

Findings

New ADHM-like methods for exceptional groups

Computed elliptic genera of 6d instanton strings

Validated methods with topological vertex and D-brane tests

Abstract

We propose new ADHM-like methods to compute the Coulomb branch instanton partition functions of 5d and 6d supersymmetric gauge theories, with certain exceptional gauge groups or exceptional matters. We study $G_2$ theories with $n_{\bf 7}\leq 3$ matters in ${\bf 7}$, and $SO(7)$ theories with $n_{\bf 8}\leq 4$ matters in the spinor representation ${\bf 8}$. We also study the elliptic genera of self-dual instanton strings of 6d SCFTs with exceptional gauge groups or matters, including all non-Higgsable atomic SCFTs with rank $2$ or $3$ tensor branches. Some of them are tested with topological vertex calculus. We also explore a D-brane-based method to study instanton particles of 5d $SO(7)$ and $SO(8)$ gauge theories with matters in spinor representations, which further tests our ADHM-like proposals.