Four-flux and warped heterotic M-theory compactifications Original Research Article

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 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 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 Newtonʹs constant is bounded from below at just the phenomenologically relevant value. However, the bound does not require an ad hoc truncation of the orbifold-size any longer. Finally we demonstrate explicitly that to leading order in κ2/3 no Cosmological constant is induced in the four-dimensional low-energy action. This is in accord with what one can expect from supersymmetry.