String Geometry and Non-perturbative Formulation of String Theory

TL;DR

This paper introduces a non-perturbative formulation of string theory based on a novel string geometry framework, unifying particles and space-time without relying on fixed backgrounds.

Contribution

It defines a background-independent superstring theory using string geometry, incorporating interactions, topologies, and metrics, and derives all-order scattering amplitudes.

Findings

Derives all-order perturbative scattering amplitudes for superstring theories.

Formulates a background-independent superstring theory with supersymmetry.

Unifies particles and space-time within a single theoretical framework.

Abstract

We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces in a target manifold. Based on the string geometry, we define Einstein-Hilbert action coupled with gauge fields, and formulate superstring theory non-perturbatively by summing over metrics and the gauge fields on the spaces of strings. This theory does not depend on backgrounds. The theory has a supersymmetry as a part of the diffeomorphisms symmetry on the superstring manifolds. We derive the all-order perturbative scattering amplitudes that possess the super moduli in type IIA, type IIB and SO(32) type I superstring theories from the single theory, by considering fluctuations around fixed backgrounds representing type IIA, type IIB and SO(32) type I perturbative vacua, respectively. The theory predicts that we can see a string if we microscopically observe not only a particle but also a point in the space-time. That is, this theory unifies particles and the space-time.