Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The sl(2n|2n)^(1) Super-Toda Lattices and the Heavenly Equations as
  Continuum Limit   The $n\to\infty$ continuum limit of super-Toda models associated with the
affine $sl(2n|2n)^{(1)}$ (super)algebra series produces $(2+1)$-dimensional
integrable equations in the ${\bf S}^{1}\times {\bf R}^2$ spacetimes. The
equations of motion of the (super)Toda hierarchies depend not only on the
chosen (super)algebras but also on the specific presentation of their Cartan
matrices. Four distinct series of integrable hierarchies in relation with
symmetric-versus-antisymmetric, null-versus-nonnull presentations of the
corresponding Cartan matrices are investigated. In the continuum limit we
derive four classes of integrable equations of heavenly type, generalizing the
results previously obtained in the literature. The systems are manifestly N=1
supersymmetric and, for specific choices of the Cartan matrix preserving the
complex structure, admit a hidden N=2 supersymmetry. The coset reduction of the
(super)-heavenly equation to the ${\bf I}\times{\bf R}^{(2)}=({\bf S}^{1}/{\bf
Z}_2)\times {\bf R}^2$ spacetime (with ${\bf I}$ a line segment) is
illustrated. Finally, integrable $N=2,4$ supersymmetrically extended models in
$(1+1)$ dimensions are constructed through dimensional reduction of the
previous systems.

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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga