Complex Analytic Torsion Forms for Torus Fibrations and Moduli Spaces

We construct analytic torsion forms for line bundles on holomorphic fibrations by tori, which are not necessarily Kähler fibrations. This is done by double transgressing the top Chern class. The forms are given in terms of Epstein zeta functions. Also, we establish a corresponding double transgression formula and an anomaly formula. The forms are investigated more closely for the universal bundle over the moduli space of polarized abelian varieties and for the bundle of Jacobians over the Teichmüller space.