GENERATING FUNCTIONAL IN CFT AND EFFECTIVE ACTION FOR 2-DIMENSIONAL QUANTUM-GRAVITY ON HIGHER-GENUS RIEMANN SURFACES

We formulate and solve the analog of the universal Conformal Ward Iden tity for the stress-energy tensor on a compact Riemann surface of genu s g > 1, and present a rigorous invariant formulation of the chiral se ctor in the induced two-dimensional gravity on higher genus Riemann su rfaces. Our construction of the action functional uses various double complexes naturally associated with a Riemann surface, with computatio ns that are quite similar to descent calculations in BRST cohomology t heory. We also provide an interpretation of the action functional in t erms of the geometry of different fiber spaces over the Teichmuller sp ace of compact Riemann surfaces of genus g > 1.