6D strings and exceptional instantons

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