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 ${n}_{\mathbf{7}}\ensuremath{\le}3$ matters in $\mathbf{7}$ and $SO(7)$ theories with ${n}_{\mathbf{8}}\ensuremath{\le}4$ matters in the spinor representation $\mathbf{8}$. 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.