Nonstandard embedding and five-branes in heterotic M theory

We construct vacua of M theory on S¹/Z₂ associated with Calabi-Yau threefolds. These vacua are appropriate for compactification to N=1 supersymmetry theories in both four and five dimensions. We allow for general E₈×E₈ gauge bundles and for the presence of five-branes. The five-branes span the four-dimensional uncompactified space and are wrapped on holomorphic curves in the Calabi-Yau manifold. Properties of these vacua, as well as of the resulting low-energy theories, are discussed. We find that the low-energy gauge group is enlarged by gauge fields that originate on the five-brane world-volumes. In addition, the five-branes increase the types of new E₈×E₈ breaking patterns allowed by the non-standard embedding. Characteristic features of the low-energy theory, such as the threshold corrections to the gauge kinetic functions, are significantly modified due to the presence of the five-branes, as compared to the case of standard or non-standard embeddings without five-branes.