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

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 $W{A}_r$ minimal models when the solution has trivial monodromy around the origin of the complex plane.

1+26 pages, published version

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Cited by in corpus (8)

• Geometric aspects of the ODE/IM correspondence
• 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
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• ODE/IM correspondence and supersymmetric affine Toda field equations
• WKB analysis of the linear problem for modified affine Toda field equations
• A short review on TBA equation and scattering amplitude/Wilson loop duality