Four-Flux and Warped Heterotic M-Theory Compactifications

TL;DR

This paper explores advanced heterotic M-theory compactifications, analyzing four-flux effects beyond first order, revealing new relations between geometry and flux, and demonstrating the absence of a cosmological constant at leading order.

Contribution

It introduces two special types of four-flux in heterotic M-theory compactifications, extending the understanding of flux-geometry relations beyond first order and addressing issues with Calabi-Yau volume behavior.

Findings

Reproduces weakly coupled heterotic string torsion relation via warped geometry.

Identifies a quadratic Calabi-Yau volume dependence that avoids negative volume issues.

Shows no cosmological constant is induced at leading order, consistent with supersymmetry.

Abstract

In the framework of heterotic M-theory compactified on a Calabi-Yau threefold 'times' an interval, the relation between geometry and four-flux is derived {\it beyond first order}. Besides the case with general flux which cannot be described by a warped geometry one is naturally led to consider two special types of four-flux in detail. One choice shows how the M-theory relation between warped geometry and flux reproduces the analogous one of the weakly coupled heterotic string with torsion. The other one leads to a {\it quadratic} dependence of the Calabi-Yau volume with respect to the orbifold direction which avoids the problem with negative volume of the first order approximation. As in the first order analysis we still find that Newton's Constant is bounded from below at just the phenomenologically relevant value. However, the bound does not require an {\it ad hoc} truncation of the orbifold-size any longer. Finally we demonstrate explicitly that to leading order in $\kappa^{2/3}$ no Cosmological Constant is induced in the four-dimensional low-energy action. This is in accord with what one can expect from supersymmetry.