Lectures on Heterotic M-Theory
Abstract
Description
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.
48 pages, Lectures presented at the TASI 2000 School on Strings, Branes and Extra Dimensions, Boulder, Co, June 3-29, 2001
48 pages, Lectures presented at the TASI 2000 School on Strings, Branes and Extra Dimensions, Boulder, Co, June 3-29, 2001