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arXiv · hep-th/9509045

Generalized Toda Field Theories

Lars Brink·Mikhail Vasiliev
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Abstract

In this paper we introduce a unified approach to Toda field theories which allows us to formulate the classes of $A_n$, $B_n$ and $C_n$ models as unique models involving an arbitrary continuous parameter $ν$. For certain values of $ν$, the model describes the standard Toda theories. For other values of $ν$ it defines a class of models that involve infinitely many fields. These models interpolate between the various standard Toda field theories. They are conformally invariant and possess infinitely many conserved higher-spin currents thus making them candidates for a new set of integrable systems. A general construction is performed, which can effectively be used for the derivation of explicit forms of particular higher-spin currents. We also study the currents in a different representation in which they are linear in the dynamical variables having, however, a non-linear Poisson bracket algebra. An explicit formula for this Poisson structure is found.

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Lars Brink, Mikhail Vasiliev. 1995-09-07. Generalized Toda Field Theories. https://doi.org/10.1016/0550-3213(95)00532-3

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