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High Energy Physics - Theory

arXiv:1805.08062 (hep-th)
[Submitted on 21 May 2018 (v1), last revised 20 Nov 2018 (this version, v2)]

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

Authors: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.
Comments: 1+26 pages, published version
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Report number: TIT/HEP-667
Cite as: arXiv:1805.08062 [hep-th]
  (or arXiv:1805.08062v2 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.1805.08062
Related DOI: https://doi.org/10.1088/1751-8121/aad63f

Submission history

From: Hongfei Shu [view email]
[v1] Mon, 21 May 2018 14:03:51 UTC (22 KB)
[v2] Tue, 20 Nov 2018 11:58:05 UTC (25 KB)
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