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

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 $A_3/{\mathbf{Z}}_2$ 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.

1+21 pages, 2 figures, Typos corrected

References in corpus (4)

• The ODE/IM Correspondence
• Form factors at strong coupling via a Y-system
• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• The Baxter's Q-operator for the W-algebra $W_N$

Cited by in corpus (10)

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• ODE/IM correspondence and the Argyres-Douglas theory
• TBA equations for the Schrödinger equation with a regular singularity
• Quantum transfer-matrices for the sausage model
• ODE/IM correspondence for affine Lie algebras: A numerical approach
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• Quantum integrability from non-simply laced quiver gauge theory
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• A short review on TBA equation and scattering amplitude/Wilson loop duality