Geometry of Higgs and Toda fields on Riemann surfaces |
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| Institution: | 1. Matematisk Institut, Århus Universitet, Ny Munkegade, DK-8000 Århus C, Denmark, USA;2. Laboratoire de Physique Mathématique, Université Montpellier II, Place E. Bataillon, 34095 Montpellier Cedex 05, France;1. TU Wien, Austria;2. Saints Cyril and Methodius University of Skopje, Macedonia;1. Institute for Theoretical and Experimental Physics, Moscow, Russia;2. Institute for Information Transmission Problems RAS (Kharkevich Institute), Bolshoy Karetny per. 19, Moscow, 127994, Russia;3. National Research University Higher School of Economics, Moscow, Russia |
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| Abstract: | 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 Wn-geometries. |
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