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arXiv · 1805.08062

Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations

Katsushi Ito·Hongfei Shu
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Abstract

The massive ODE/IM correspondence is a relation between the linear problem associated with modified affine Toda field equations and two-dimensional massive integrable models. We study the massive ODE/IM correspondence for the $A_r^{(1)}$-type modified affine Toda field equations. Based on the $\psi$-system satisfied by the solutions of the linear problem, we derive the Bethe ansatz equations and determine the asymptotic behavior of the Q-functions for large value of the spectral parameter. We derive the non-linear integral equations for the Q-functions from the Bethe ansatz equations. We compute the effective central charge in the UV limit, which is identified with the one of the non-unitary $WA_r$ minimal models when the solution has trivial monodromy around the origin of the complex plane.

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Katsushi Ito, Hongfei Shu. 2018-05-21. Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations. https://doi.org/10.1088/1751-8121/aad63f

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