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.
Highlights
Instantons are semiclassical representations of nonperturbative quantum phenomena
We study the elliptic genera of self-dual instanton strings of 6D superconformal field theories (SCFTs) with exceptional gauge groups or matters, including all non-Higgsable atomic SCFTs with rank 2 or 3 tensor branches
We find that the following extra fields, taking the forms of N 1⁄4 ð0; 2Þ chiral or Fermi multiplets, yield the right physics2: 2Our motivation behind introducing this ansatz for the UV theory is described below (2.2)
Summary
Instantons are semiclassical representations of nonperturbative quantum phenomena. In Yang-Mills gauge theories, instantons given by self-dual gauge fields on R4 play important roles in various contexts. Open strings can engineer matters in the fundamental or rank 2 product representations This gives the notion of “classical matters,” whose inclusion to the instanton moduli space dynamics still admits ADHM description. We start from Hr classical ADHM construction, and add more world volume matters and interactions to suit the physics They are motivated by [4], where 2D gauge theories were found for the instanton strings of non-Higgsable 6D SUð3Þ gauge theories.
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