Enlarging the Parameter Space of Heterotic M-Theory Flux Compactifications to Phenomenological Viability

TL;DR

This work shows that the small-$\epsilon$ constraint in heterotic M-theory flux compactifications is not mandatory when the exact non-linear 11d background is used. By incorporating G-flux and boundary/M5 sources, the authors derive a non-singular warp-factor and a positive CY volume, and prove the tree-level cosmological constant vanishes due to supersymmetry. They establish the 11d origin of the 5d domain-wall solution and demonstrate how Newton's constant can be predicted in both standard vacua and setups with M5-brane stabilization, bringing theoretical values in line with experiment. Overall, the approach expands the phenomenological viability of heterotic M-theory by leveraging non-linear background effects that preserve SUSY and align with low-energy observables.

Abstract

Heterotic M-Theory is a promising candidate for that corner of M-theory which makes contact with the real world. However, while the theory requires one of its expansion parameters, $ε$, to be perturbatively small, a successful phenomenology requires $ε= {\cal O}(1)$. We show that the constraint to have small $ε$ is actually unnecessary: instead of the original flux compactification background valid to linear order in $ε$ one has to use its appropriate non-linear extension, the exact background solution. The exact background is determined by supersymmetry and consequently one expects the tree-level cosmological constant to vanish which we demonstrate in detail, thereby verifying once more the consistency of this background. Furthermore we show that the exact background represents precisely the 11d origin of the 5d domain wall solution which is an exact solution of the effective 5d heterotic M-theory. We also comment on singularities and the issue of chirality changing transitions in the exact background. The exact background is then applied to determine Newton's Constant for vacua with an M5 brane on the basis of a recent stabilization mechanism for the orbifold length. For vacua without M5 brane we obtain a correction to the lower bound on Newton's Constant which brings it in perfect agreement with the measured value.

Figures (3)

• Figure 1: The left figure shows the positive parabolic CY volume which results from using the exact non-linear background in comparison to the linearized approximation which is given as the tangent to the parabola at the location of the visible boundary. The right figure compares the exact warp-factor $e^f$ (curve with the peak at the singularity) with the linearized warp-factor $1+f_{lin}$ (straight line). To trust the linearized approximations requires $x^{11}{\cal{S}} _v \ll 1$ which is only valid in the constrained parameter regime where $\epsilon\ll 1$. This constraint is not needed when one works with the exact background.
• Figure 2: The diagram of connections between various heterotic M-theory backgrounds in 11d and 5d.
• Figure 3: The 4d Newton's Constant $G_4(L)$ is shown evaluated in the exact non-linear background (\ref{['MetricSol']}). $G_{4,c} = G_4(L = 1/{\cal{S}} _v)$ is the value at the point where the CY volume vanishes. Because in this background the CY volume stays non-negative for all values of the orbifold size $L$ likewise $G_4$ stays positive for all $L$.