ODE/IM correspondence and Bethe ansatz for affine Toda field equations

ODE/IM correspondence and Bethe ansatz for affine Toda field equations

We study the linear problem associated with modified affine Toda field equation for the Langlands dual gˆ∨, where gˆ is an untwisted affine Lie algebra. The connection coefficients for the asymptotic solutions of the linear problem are found to correspond to the Q-functions for g-type quantum integr...

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Main Authors: Katsushi Ito, Christopher Locke
Format: Article
Language:English
Published: Elsevier 2015-07-01
Series:Nuclear Physics B
Online Access:http://www.sciencedirect.com/science/article/pii/S0550321315001765
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spelling doaj-0e3402aaeab045e6af2cc865f870c3102020-11-24T22:37:30ZengElsevierNuclear Physics B0550-32131873-15622015-07-01896C76377810.1016/j.nuclphysb.2015.05.016ODE/IM correspondence and Bethe ansatz for affine Toda field equationsKatsushi ItoChristopher LockeWe study the linear problem associated with modified affine Toda field equation for the Langlands dual gˆ∨, where gˆ is an untwisted affine Lie algebra. The connection coefficients for the asymptotic solutions of the linear problem are found to correspond to the Q-functions for g-type quantum integrable models. The ψ-system for the solutions associated with the fundamental representations of g leads to Bethe ansatz equations associated with the affine Lie algebra gˆ. We also study the A2r(2) affine Toda field equation in massless limit in detail and find its Bethe ansatz equations as well as T–Q relations.http://www.sciencedirect.com/science/article/pii/S0550321315001765
collection DOAJ
language English
format Article
sources DOAJ
author Katsushi Ito
Christopher Locke
spellingShingle Katsushi Ito
Christopher Locke
ODE/IM correspondence and Bethe ansatz for affine Toda field equations
Nuclear Physics B
author_facet Katsushi Ito
Christopher Locke
author_sort Katsushi Ito
title ODE/IM correspondence and Bethe ansatz for affine Toda field equations
title_short ODE/IM correspondence and Bethe ansatz for affine Toda field equations
title_full ODE/IM correspondence and Bethe ansatz for affine Toda field equations
title_fullStr ODE/IM correspondence and Bethe ansatz for affine Toda field equations
title_full_unstemmed ODE/IM correspondence and Bethe ansatz for affine Toda field equations
title_sort ode/im correspondence and bethe ansatz for affine toda field equations
publisher Elsevier
series Nuclear Physics B
issn 0550-3213
1873-1562
publishDate 2015-07-01
description We study the linear problem associated with modified affine Toda field equation for the Langlands dual gˆ∨, where gˆ is an untwisted affine Lie algebra. The connection coefficients for the asymptotic solutions of the linear problem are found to correspond to the Q-functions for g-type quantum integrable models. The ψ-system for the solutions associated with the fundamental representations of g leads to Bethe ansatz equations associated with the affine Lie algebra gˆ. We also study the A2r(2) affine Toda field equation in massless limit in detail and find its Bethe ansatz equations as well as T–Q relations.
url http://www.sciencedirect.com/science/article/pii/S0550321315001765
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AT christopherlocke odeimcorrespondenceandbetheansatzforaffinetodafieldequations
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