Fundamental structure of string geometry theory

TL;DR

String geometry theory provides a non-perturbative framework in which a generalized T-symmetry fixes the classical action and decouples $eta$-dependent tree-level effects from $Hbar$-dependent loops. It shows that all-order perturbative string amplitudes can be derived from tree-level data and proves a non-renormalization theorem that eliminates loop corrections, while non-perturbative instantons yield corrections of order $e^{-1/g_s^2}$ that drive vacuum transitions. The true vacuum is proposed to be the minimum of the classical potential restricted to perturbative vacua, with Wheeler–DeWitt constraints governing background dynamics and instanton tunneling providing the non-perturbative mechanism for vacuum selection. By connecting the landscape of perturbative vacua to a geometrically organized background and a calculable potential, the work aims to extract phenomenological consequences and guide the search for a realistic 4D effective theory.

Abstract

String geometry theory is one of the candidates of a non-perturbative formulation of string theory. In this theory, the ``classical'' action is almost uniquely determined by T-symmetry, which is a generalization of the T-duality, where the parameter of ``quantum'' corrections $β$ in the path-integral of the theory is independent of that of quantum corrections $\hbar$ in the perturbative string theories. We distinguish the effects of $β$ and $\hbar$ by putting " " like "classical" and "loops" for tree level and loop corrections with respect to $β$, respectively, whereas by putting nothing like classical and loops for tree level and loop corrections with respect to $\hbar$, respectively. A non-renormalization theorem states that there is no ``loop'' correction. Thus, there is no problem of non-renormalizability, although the theory is defined by the path-integral over the fields including a metric on string geometry. No ``loop'' correction is also the reason why the complete path-integrals of the all-order perturbative strings in general string backgrounds are derived from the ``tree''-level two-point correlation functions in the perturbative vacua, although string geometry includes information of genera of the world-sheets of the stings. Furthermore, a non-perturbative correction in string coupling with the order $e^{-1/g_s^2}$ is given by a transition amplitude representing a tunneling process between the semi-stable vacua in the ``classical'' potential by an ``instanton'' in the theory. From this effect, a generic initial state will reach the minimum of the potential.

Figures (3)

• Figure 1: Various string states. The red and blue lines represent one string and two strings, respectively.
• Figure 2: A super loop diagram
• Figure 3: Cancellation between the bosonic and fermionic loop diagrams