96-407 Ettore Aldrovandi and Leon A. Takhtajan

Generating Functional in CFT and Effective Action for Two-dimensional Quantum Gravity on Higher Genus Riemann Surfaces (57K, Latex2e + AmsLatex1.2 + epsf.sty) Sep 9, 96

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Abstract. We formulate and solve the analog of the universal Conformal Ward Identity for the stress-energy tensor on a compact Riemann surface of genus $g>1$, and present a rigorous invariant formulation of the chiral sector in the induced two-dimensional gravity on higher genus Riemann surfaces. Our construction of the action functional uses various double complexes naturally associated with a Riemann surface, with computations that are quite similar to descent calculations in BRST cohomology theory.

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