A Mumford form on infinite Grassmannians

The Polyakov measure in bosonic string theory can be expressed in terms of the Mumford form, which is a trivializing section of a product of determinant line bundles over the moduli space of genus g curves. We will discuss the work in https://arxiv.org/abs/2412.18570, which reviews how the moduli space can be embedded in an infinite dimensional Grassmannian as a Virasoro orbit and generalizes the Mumford form to other such orbits. In particular, this “universal Mumford form” can be described in terms of coordinates in the Grassmannian, which are amenable to computation and thus could have implications to the evaluation of amplitudes.