String geometry phenomenology
Matsuo Sato, Maki Takeuchi
TL;DR
The paper tests a non-perturbative approach from string geometry theory to identify the true vacuum by minimizing the potential for string backgrounds in a simple heterotic non-supersymmetric setup. It derives an explicit effective potential for free parameters by embedding a flux-filled, product-space internal geometry and solving for the scalar mode $\boldsymbol{φ}$ via a Green-function expansion, followed by a numerical minimization that yields a precise minimum at $b\bar{Λ} \approx 1.80308$. This minimum translates into a nontrivial relation between the compactification scale and flux quanta, and for three generations the model requires $M_c < M_s$ with a minimal flux-sum of $\sum_{A,i} n_{Ai}^2 = 5$. The results illustrate how non-perturbative string geometry constraints can connect internal-geometric data to observable phenomenology and guide searches for vacua close to the true string vacuum in the landscape.
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.