Phenomenology of nonstandard embedding and five-branes in M theory

We study the phenomenology of the strong-coupling limit of $E_8\times E_8$ heterotic string obtained from M theory, using Calabi-Yau compactification. After summarizing the standard embedding results, we concentrate on nonstandard embedding vacua as well as vacua where nonperturbative objects such as five-branes are present. We analyze in detail the different scales of the theory, 11-dimensional Planck mass, compactification scale, and 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 $\left(\approx {10}^{11}\hspace{0.5em}\mathrm{GeV}\right)$ or 1 TeV values or to obtain the radius of the orbifold as large as a millimeter 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 weakly coupled heterotic string.