Geometry of Higgs and Toda Fields on Riemann Surfaces

Details Geometry of Higgs and Toda Fields on Riemann Surfaces Geometry of Higgs and Toda Fields on Riemann Surfaces

1993-12-11

arxiv.org/abs/hep-th/9312093v2

J.Geom.Phys. 17 (1995) 25-48

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, LaTeX+AMSFonts (One section and a few comments added) Aar. Mat. Inst. Prep. 1993/32 -- Montpellier PM/93--43

Scientific paper

10.1016/0393-0440(94)00038-6

We discuss geometrical aspects of Higgs systems and Toda field theory in the framework of the theory of vector bundles on Riemann surfaces of genus greater than one. We point out how Toda fields can be considered as equivalent to Higgs systems -- a connection on a vector bundle $E$ together with an End($E$)--valued one form both in the standard and in the Conformal Affine case. We discuss how variations of Hodge structures can arise in such a framework and determine holomorphic embeddings of Riemann surfaces into locally homogeneous spaces, thus giving hints to possible realizations of $W_n$--geometries. }

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