| We start this work by reinterpreting the Moduli problem of stable parabolic bundles from a complex analytic perspective. This allows us to introduce canonical complex coordinates on the Moduli space, analogous to the Bers' coordinates on Teichmuller spaces. Similarly, a suitable analog of uniformization will play a central role. Finally, the identification of the tangent space at a point with a certain space of automorphic forms leads to the introduction of the parabolic Narasimhan-Atiyah-Bott metric on the Moduli space, which is analogous to the Weil-Petersson metric. Secondly, for each stable parabolic bundle, a regularized WZNW action functional is defined on the space of singular Hermitian metrics with prescribed asymptotics at a finite set of points in the sphere. We prove that these functionals evaluated at their extrema gives rise to a function on the Moduli space that is a Kahler potential for the parabolic Narasimhan-Atiyah-Bott metric over a certain analytic open subset. |
