String geometry phenomenology

TL;DR

This paper explores string geometry theory to identify the true vacuum in string theory by analyzing a specific heterotic model with flux compactifications, deriving constraints between compactification scale and flux quanta.

Contribution

It provides an explicit analysis of a heterotic string model with flux compactification, linking potential minima to physical parameters and advancing understanding of the string landscape.

Findings

Derived a constraint between compactification scale and flux quanta.

Identified local minima of the potential in a heterotic model.

Connected potential minima to the true vacuum in string theory.

Abstract

Recently, a potential for string backgrounds is obtained from string geometry theory, which is a candidate for the non-perturbative formulation of string theory. By substituting a string phenomenological model with free parameters to the potential, one obtains a potential for the free parameters, whose minimum determines the free parameters. The model with the determined parameters is the ground state in the model. This will be the local minimum in a partial region of the model in the string theory landscape. By comparing it with the other local minimum, one can determine which model is near the minimum of the potential for string backgrounds, that will be the true vacuum in string theory, in the sense of the values of the potential. We will be able to find the true vacuum in string theory through a series of such researches. In this paper, we perform this analysis of a certain simple heterotic non-supersymmetric model explicitly, where the six-dimensional internal spaces are products of two-dimensional spaces of constant curvatures, and the generation number of massless fermions is given by the flux quantization numbers. As a result, we obtain a constraint between the compactification scale and the flux quanta.