Fermi-gas correlators of ADHM theory and triality symmetry

TL;DR

This paper analytically investigates the sphere correlation functions in 3d ADHM theory, revealing a hidden triality symmetry that constrains perturbative coefficients and connects to M-theory dualities.

Contribution

It uncovers a hidden triality symmetry in the Fermi-gas formulation of ADHM theory's correlation functions, providing analytical insights into perturbative corrections.

Findings

Leading coefficients are invariant under triality symmetry.

Triality symmetry constrains next-to-leading corrections.

Connection to twisted M-theory and M2-brane configurations.

Abstract

We analytically study the Fermi-gas formulation of sphere correlation functions of the Coulomb branch operators for 3d $\mathcal{N}=4$ ADHM theory with a gauge group $U(N)$, an adjoint hypermultiplet and $l$ hypermultiplets which can describe a stack of $N$ M2-branes at $A_{l-1}$ singularities. We find that the leading coefficients of the perturbative grand canonical correlation functions are invariant under a hidden triality symmetry conjectured from the twisted M-theory. The triality symmetry also helps us to fix the next-to-leading corrections analytically.