Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher Grading Conformal Affine Toda Teory and (Generalized)
  Sine-Gordon/Massive Thirring Duality   Some properties of the higher grading integrable generalizations of the
conformal affine Toda systems are studied. The fields associated to the
non-zero grade generators are Dirac spinors. The effective action is written in
terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine
Lie algebra, and an off-critical theory is obtained as the result of the
spontaneous breakdown of the conformal symmetry. Moreover, the off-critical
theory presents a remarkable equivalence between the Noether and topological
currents of the model. Related to the off-critical model we define a real and
local Lagrangian provided some reality conditions are imposed on the fields of
the model. This real action model is expected to describe the soliton sector of
the original model, and turns out to be the master action from which we uncover
the weak-strong phases described by (generalized) massive Thirring and
sine-Gordon type models, respectively. The case of any (untwisted) affine Lie
algebra furnished with the principal gradation is studied in some detail.
  The example of $\hat{sl}(n) (n=2,3)$ is presented explicitly.

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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: math
3
The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio