ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation

TL;DR

This paper explores the massive ODE/IM correspondence for a modified affine Toda field equation, deriving Bethe ansatz equations and analyzing T-/Y-systems with monodromy effects, supported by numerical studies.

Contribution

It extends the ODE/IM correspondence to the modified $B_2^{(1)}$ affine Toda system, establishing new relations with the $A_3/{f Z}_2$ integrable system and analyzing boundary conditions.

Findings

Derived Bethe ansatz equations from the $ ext{psi}$-system.

Established relations between T-/Y-systems and $A_3/{f Z}_2$ system.

Numerical analysis of high-temperature limit and monodromy effects.

Abstract

We study the massive ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation. Based on the $\psi$-system for the solutions of the associated linear problem, we obtain the Bethe ansatz equations. We also discuss the T-Q relations, the T-system and the Y-system, which are shown to be related to those of the $A_3/{\bf Z}_2$ integrable system. We consider the case that the solution of the linear problem has a monodromy around the origin, which imposes nontrivial boundary conditions for the T-/Y-system. The high-temperature limit of the T- and Y-system and their monodromy dependence are studied numerically.