Bethe Ansatz equations for the classical $A_n^{(1)}$ affine Toda field theories

Abstract

We establish a correspondence between classical $A_n^{(1)}$ affine Toda field theories and $A_n$ Bethe Ansatz systems. We show that the connection coefficients relating specific solutions of the associated classical linear problem satisfy functional relations of the type that appear in the context of the massive quantum integrable model.

13 pages. V2: fixed typos and described Lax pair for modified equations in more detail

References in corpus (2)

• 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 (16)

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• Bethe Ansatz and the Spectral Theory of affine Lie algebra--valued connections II. The non simply--laced case
• Geometric aspects of the ODE/IM correspondence
• Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence
• TBA equations for the Schrödinger equation with a regular singularity
• ODE/IM correspondence and Bethe ansatz for affine Toda field equations
• WKB periods for higher order ODE and TBA equations
• Wall-crossing of TBA equations and WKB periods for the third order ODE
• ODE/IM correspondence for affine Lie algebras: A numerical approach
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• ODE/IM correspondence and supersymmetric affine Toda field equations
• Elementary functions in Thermodynamic Bethe Ansatz
• WKB analysis of the linear problem for modified affine Toda field equations
• Integrals of motion in conformal field theory with W-symmetry and the ODE/IM correspondence