String Geometry and Non-perturbative Formulation of String Theory

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.

92 pages, 5 figures, minor changes, references added

References in corpus (2)

• Ghost D-branes
• Moduli Space in Homological Mirror Symmetry

Cited by in corpus (6)

• The "emerging" reality from "hidden" spaces
• Topological String Geometry
• Perturbative string theory from Newtonian limit of string geometry theory
• String Backgrounds in String Geometry
• Path-integrals of perturbative superstrings on curved backgrounds from string geometry theory
• T-symmetry in String Geometry Theory