Abstract
The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific S U ( 4 ) vector bundle leading to the “heterotic standard model” in the observable sector. A generic formalism for a consistent hidden sector gauge bundle, within the context of strongly coupled heterotic M-theory, is presented. Anomaly cancellation and the associated bulk space 5-branes are discussed in this context. The further compactification to a 4-dimensional effective field theory on a linearized BPS double domain wall is then presented to order κ 11 4 / 3 . Specifically, the generic constraints required for anomaly cancellation and by the linearized domain wall solution, restrictions imposed by the vanishing of the D-terms and, finally, the constraints imposed by the necessity for positive, perturbative squared gauge couplings to this order are presented in detail.
Highlights
One of the major prerogatives of the Large Hadron Collider (LHC) at CERN is to search for low-energy N = 1 supersymmetry
It has long been known that specific vacua of both the weakly coupled [1,2] and strongly coupled [3,4,5] E8 × E8 heterotic superstring can produce effective theories with at least a quasi-realistic particle spectrum exhibiting N = 1 supersymmetry [6,7,8,9,10]
We present the precise constraints required by such a vacuum within the context of heterotic strongly coupled M-theory
Summary
Symmetry 2018, 10, 723 papers on the heterotic standard model, in analogy with the KKLT mechanism [38] in Type II string theory, allowed the hidden sector to contain an anti-5-brane– explicitly breaking N = 1 supersymmetry [39,40] This was done so that the potential energy could admit a meta-stable de Sitter space vacuum. We consider a specific set of vacua for which the hidden sector vector bundle is restricted to be the Whitney sum of one non-Abelian SU ( N ) bundle with a single line bundle, while allowing only one five-brane in the bulk space Under these circumstances, the constraint equations greatly simplify and are explicitly presented. We demonstrate how the parameters associated with these bundles are computed for a specific choice of these objects
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