Path integrals of perturbative strings on curved backgrounds from string geometry theory

TL;DR

This paper derives path integrals for all orders of perturbative strings on various curved backgrounds within string geometry theory, aiming to contribute to the non-perturbative understanding of string theory.

Contribution

It introduces a method to obtain path integrals of perturbative strings on arbitrary backgrounds from string geometry theory, expanding the non-perturbative framework.

Findings

Path integrals derived for all orders of perturbative strings.

Applicable to general curved backgrounds with metric, B-field, and dilaton.

Provides a foundation for non-perturbative string theory formulations.

Abstract

String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, from the closed bosonic sector of string geometry theory, we derive path integrals of all order perturbative strings on all the string backgrounds, $G_{\mu\nu}(x)$, $B_{\mu\nu}(x)$, and $\Phi (x)$, by considering fluctuations around the string background configurations, which are parametrized by the string backgrounds.