The potential for string backgrounds from string geometry theory (2309.10394v3)

Abstract: String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, in the bosonic closed sector of string geometry theory, we identify string background configurations, which include general string backgrounds in bosonic closed string theory. From fluctuations around these configurations, we derive the path-integrals of perturbative strings on the string backgrounds up to any order. Furthermore, the identification of the string background configurations enables us to obtain differential equations that determine a potential for string backgrounds. We obtain a potential for perturbative vacua in string theory by substituting the string background configurations into the classical potential in string geometry theory and imposing the differential equations by the method of Lagrange multipliers. We also solve these differential equations and obtain a potential explicitly up to the second order without Lagrange multipliers.