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

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.