Conformal field theory and the Kaehler geometry of moduli spaces

An interesting property of the Liouville theory on punctured 2-spheres is
that the evaluation of the Liouville action functional at its extrema (the
hyperbolic metrics) gives rise to a Kaehler potential for the Weil-Petersson
metric on their Teichmuller space. In this talk I will explain how this result
can be reproduced on a unitary character variety, corresponding to the
moduli space of parabolic bundles over the sphere, by means of a suitable
interpretation of the WZNW action functional.