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

A bstract 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.