Quantum symmetries in supersymmetric Toda theories
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Abstract:
: We consider two--dimensional supersymmetric Toda theories based on the Lie superalgebras , and which admit a fermionic set of simple roots and a fermionic untwisted affine extension. In particular, we concentrate on two simple examples, the and theories. Both in the conformal and massive case we address the issue of quantum integrability by constructing the first non trivial conserved currents and proving their conservation to all--loop orders. While the and systems are genuine supersymmetric theories, the models possess a global supersymmetry. In the conformal case, we show that the stress--energy tensor, uniquely determined by the holomorphicity condition, has vanishing central charge and it corresponds to the stress--energy tensor of the associated topological theory. (Invited talk at the International Workshop ``String theory, quantum gravity and the unification of the fundamental interactions'', Roma, September 1992)- talk
- field theory: Toda
- supersymmetry
- dimension: 2
- integrability
- tensor: energy-momentum
- central charge
- field theory: topological
- current: conservation law
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