Liouville and Toda field theories on Riemann surfaces

Details Liouville and Toda field theories on Riemann surfaces Liouville and Toda field theories on Riemann surfaces

1993-03-10

arxiv.org/abs/hep-th/9303064v1

J. Geom. Phys. 14 (1994) 65-109

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, LaTeX, SISSA-ISAS 27/93/EP

Scientific paper

10.1016/0393-0440(94)90054-X

We study the Liouville theory on a Riemann surface of genus g by means of their associated Drinfeld--Sokolov linear systems. We discuss the cohomological properties of the monodromies of these systems. We identify the space of solutions of the equations of motion which are single--valued and local and explicitly represent them in terms of Krichever--Novikov oscillators. Then we discuss the operator structure of the quantum theory, in particular we determine the quantum exchange algebras and find the quantum conditions for univalence and locality. We show that we can extend the above discussion to $sl_n$ Toda theories.

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