1993/03/17 by Kenichiro Aoki, Eric D'Hoker, Aoki, Kenichiro +1
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.hep-th/9303094
19 pages
arxiv created 1993/03/17 · arxiv updated 2009/11/30
We generalize the Lax pair and Bäcklund 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.)