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arXiv · 1312.6759

ODE/IM correspondence and modified affine Toda field equations

Katsushi Ito·Christopher Locke
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Abstract

We study the two-dimensional affine Toda field equations for affine Lie algebra $\hat{\mathfrak{g}}$ modified by a conformal transformation and the associated linear equations. In the conformal limit, the associated linear problem reduces to a (pseudo-)differential equation. For classical affine Lie algebra $\hat{\mathfrak{g}}$, we obtain a (pseudo-)differential equation corresponding to the Bethe equations for the Langlands dual of the Lie algebra $\mathfrak{g}$, which were found by Dorey et al. in study of the ODE/IM correspondence.

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Katsushi Ito, Christopher Locke. 2014-04-16. ODE/IM correspondence and modified affine Toda field equations. https://doi.org/10.1016/j.nuclphysb.2014.06.007

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