Geometrical origin of integrability for Liouville and Toda theory

Details Geometrical origin of integrability for Liouville and Toda theory Geometrical origin of integrability for Liouville and Toda theory

1993-03-17

arxiv.org/abs/hep-th/9303094v1

Physics

High Energy Physics

High Energy Physics - Theory

19 pages

Scientific paper

We generalize the Lax pair and B\"acklund transformations for Liouville and Toda field theories as well as their supersymmetric generalizations, to the case of arbitrary Riemann surfaces. We make use of the fact that Toda field theory arises naturally and geometrically in a restriction of so called $W$--geometry to ordinary Riemannian geometry. This derivation sheds light on the geometrical structure underlying complete integrability of these systems. (Invited talk presented at the 877th meeting of the American Mathematical Society, USC, November 1992 and at the YITP workshop ``Directions on Quantum Gravity", Kyoto, November 1992.)

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