The perturbative vacua in string geometry theory

TL;DR

This work identifies perturbative vacua in the bosonic closed sector of string geometry theory and derives perturbative string path-integrals on general backgrounds to all orders by analyzing fluctuations around these vacua. By formulating a background-restricted classical potential and enforcing on-shell conditions with Lagrange multipliers, it yields a multi-local potential $V_{\rm string}$ that encodes the string theory landscape, with true vacua corresponding to minima. In the perturbative regime, the approach reproduces the standard worldsheet action through a Schwinger-representation of the propagator and yields the familiar path-integral $S_{s}$ for strings on $G_{\mu\nu}(x)$, $B_{\mu\nu}(x)$, and $\Phi(x)$. The authors discuss extending to supersymmetric cases and propose strategies to locate global minima (e.g., Calabi–Yau compactifications, Regge calculus) with potential implications for internal geometry, flux configurations, and connections to the Standard Model and cosmology.

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 completely identify the perturbative vacua, 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.

Figures (2)

• Figure 1: Various string states. The red and blue lines represent one string and two strings, respectively.
• Figure 2: A path and a Riemann surface. The line on the left is a trajectory in the path integral. The trajectory parametrized by $\bar{\tau}$ from $-\infty$ to $\infty$, represents a Riemann surface with fixed punctures in $\mathcal{M}$ on the right.