Equivariant Bott-Chern currents and the Ray-Singer analytic torsion (Q1824268)

In this paper, we show that, at least formally, the Ray-Singer analytic torsion of a holomorphic Hermitian vector bundle can be expressed as the integral on the loop space of a Bott-Chern equivariant current naturally associated to the immersion of the considered manifold in its loop space. Such currents are studied in a finite dimensional context. They are then shown to exhibit the same properties as the Quillen metrics on determinants of the cohomology, including at the level of intermediary computations.