Lectures on heterotic M-theory

We present three lectures on heterotic M-theory and a fourth lecture extending this theory to more general orbifolds. In Lecture 1, Horava-Witten theory is briefly discussed. We then compactify this theory on Calabi-Yau threefolds, choosing the "standard" embedding of the spin connection in the gauge connection. We derive, in detail, both the five-dimensional effective action and the associated actions of the four-dimensional "end-of-the-world" branes. Lecture 2 is devoted to showing that this theory naturally admits static, N = 1 supersymmetry preserving BPS three-branes, the minimal vacuum having two such branes. One of these, the "visible" brane, is shown to support a three-generation E-6 grand unified theory, whereas the other emerges as the "hidden" brane with unbroken E-8 gauge group. Thus heterotic M-theory emerges as a fundamental paradigm for so-called "brane world" scenarios of particle physics. In Lecture 3, we introduce the concept of "non-standard" embeddings. These are shown to permit a vast generalization of allowed vacua, leading on the visible brane to new grand unified theories, such as SO(10) and SU(5), and to the standard model SU(3)(C) x SU(2)(L) X U(1)(Y). It is demonstrated that non-standard embeddings generically imply the existence of five-branes in the bulk space. The physical properties of these bulk branes is discussed in detail. Finally, in Lecture 4 we move beyond Horava-Witten theory and consider orbifolds larger than S-1/Z(2), For explicitness, we consider M-theory orbifolds on S-1/Z(2) x T-4/Z(2), discussing their anomaly structure in detail and completely determining both the untwisted and twisted sector spectra.