Grassmannian and string theory

TL;DR

This paper explores the potential of infinite-dimensional Grassmannian manifolds as a framework for non-perturbative string theory, proposing new mathematical structures and conjectures linking Grassmannians to string amplitudes and dualities.

Contribution

It introduces the idea of using Grassmannians as generalized moduli spaces for string theory and proposes formal definitions of string amplitudes within this framework.

Findings

Grassmannians can be viewed as generalized moduli spaces for string theory.

A formal approach to defining string amplitudes using Grassmannian structures.

A proposed involution on Grassmannian related to S-duality in string theory.

Abstract

Infinite-dimensional Grassmannian manifold contains moduli spaces of Riemann surfaces of all genera. This well known fact leads to a conjecture that non-perturbative string theory can be formulated in terms of Grassmannian. We present new facts supporting this hypothesis. In particular, it is shown that Grassmannians can be considered as generalized moduli spaces; this statement permits us to define corresponding "string amplitudes" (at least formally). One can conjecture, that it is possible to explain the relation between non-perturbative and perturbative string theory by means of localization theorems for equivariant cohomology; this conjecture is based on the characterization of moduli spaces, relevant to string theory, as sets consisting of points with large stabilizers in certain groups acting on Grassmannian. We describe an involution on the Grassmannian that could be related to S-duality in string theory.