Phenomenology of nonstandard embedding and five-branes in M theory

Abstract

We study the phenomenology of the strong-coupling limit of $E_8\times E_8$ heterotic string obtained from M-theory, using a Calabi-Yau compactification. After summarizing the standard embedding results, we concentrate on non-standard embedding vacua as well as vacua where non-perturbative objects as five-branes are present. We analyze in detail the different scales of the theory, eleven-dimensional Planck mass, compactification scale, orbifold scale, and how they are related taking into account higher order corrections. To obtain the phenomenologically favored GUT scale is easier than in standard embedding vacua. To lower this scale to intermediate ($\approx 10^{11}$ GeV) or 1 TeV values or to obtain the radius of the orbifold as large as a millimetre is possible. However, we point out that these special limits are unnatural. Finally, we perform a systematic analysis of the soft supersymmetry-breaking terms. We point out that scalar masses larger than gaugino masses can easily be obtained unlike the standard embedding case and the weakly-coupled heterotic string.