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

TL;DR

This paper demonstrates that using the exact non-linear background in heterotic M-theory allows for phenomenologically viable flux compactifications with large parameters, aligning theoretical models with observed gravitational constants.

Contribution

It introduces the use of exact non-linear backgrounds in heterotic M-theory, enabling phenomenologically viable flux compactifications without the small parameter constraint.

Findings

Exact background solutions have vanishing tree-level cosmological constant.

The exact background corresponds to the 11d origin of 5d domain wall solutions.

Corrected Newton's Constant aligns with observed values.

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, $\epsilon$, to be perturbatively small, a successful phenomenology requires $\epsilon = {\cal O}(1)$. We show that the constraint to have small $\epsilon$ is actually unnecessary: instead of the original flux compactification background valid to linear order in $\epsilon$ 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.