Weil-Petersson forms for families of polystable bundles over compact Kahler manifolds

The moduli space of polystable holomorphic vector bundles over a compact Kahler manifold previously constructed by the authors is equipped with a positive closed current that possesses local continuous potentials, these given by explicit integral formulae. Its restriction to the moduli space of stable holomorphic vector bundles is the classical Weil-Petersson form. On an open dense subspace of the polystable moduli space it is equal to a semi-classical smooth Weil-Petersson form.