Defects and type D relativistic Toda lattice for some 5d gauge theories

TL;DR

This paper explores the connection between type D relativistic Toda lattices and 5d gauge theories, using a folded ADHM construction to relate instanton moduli spaces and Bethe gauge correspondence.

Contribution

It introduces a novel folding of the ADHM construction for SO groups and establishes a new Bethe gauge correspondence with type D Toda lattices.

Findings

Young diagram description for SO instantons

Proof that the regular monodromy defect corresponds to the Toda lattice wavefunction

Establishment of the Bethe gauge correspondence for folded theories

Abstract

We perform folding on the ADHM construction of the instanton moduli space from $SU$ to $SO$ group. A Young diagram description for the $SO$ instanton is obtained after modifying the real and complex moment maps of the ADHM data. We study the Bethe gauge correspondence between type D relativistic Toda lattice and 5d $\mathcal{N}=1$ folded theory. In particular we prove that the regular monodromy defect in the folded gauge theory is the stationary wavefunction of the type D relativistic Toda lattice.