6D strings and exceptional instantons

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(7) <= 3 matters in 7 and SO(7) theories with n(8) <= 4 matters in the spinor representation 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.