Toward the Universal Mumford form on Sato Grassmannians

TL;DR

This paper constructs universal Mumford forms on Sato Grassmannians and super Sato Grassmannians using Virasoro and Neveu-Schwarz algebra flows, advancing the understanding of these spaces in string theory.

Contribution

It introduces a novel approach using algebra flows to build universal Mumford forms, offering an alternative to KP flow methods and extending to super Sato Grassmannians.

Findings

Constructed a local universal Mumford form on Sato Grassmannians.

Extended the construction to super Sato Grassmannians with Neveu-Schwarz algebra.

Demonstrated the relevance to string theory moduli spaces.

Abstract

We construct a local universal Mumford form on a product of Sato Grassmannians using the flow of the Virasoro algebra. The existence of this universal Mumford form furthers the proposal that the Sato Grassmannian provides a universal moduli space with applications to string theory. Our approach using the Virasoro flow is an alternative to using the KP flow, which in particular allows for a bosonic universal Mumford form to be constructed. Applying the same method, we construct a local universal super Mumford form on a product of super Sato Grassmannians using the flow of the Neveu-Schwarz algebra.