TASI lectures: special holonomy in string theory and M-theory
Abstract
Description
A brief, example-oriented introduction is given to special holonomy and its uses in string theory and M-theory. We discuss A_k singularities and their resolution; the construction of a K3 surface by resolving T^4/Z_2; holomorphic cycles, calibrations, and worldsheet instantons; aspects of the low-energy effective action for string compactifications; the significance of the standard embedding of the spin connection in the gauge group for heterotic string compactifications; G_2 holonomy and its relation to N=1 supersymmetric compactifications of M-theory; certain isolated G_2 singularities and their resolution; the Joyce construction of compact manifolds of G_2 holonomy; the relation of D6-branes to M-theory on special holonomy manifolds; gauge symmetry enhancement from light wrapped M2-branes; and chiral fermions from intersecting branes. These notes are based on lectures given at TASI '01.
34 pages, 9 figures, latex. Lectures delivered at TASI '01. v2: more printer-friendly, refs added. v3: some typos corrected
34 pages, 9 figures, latex. Lectures delivered at TASI '01. v2: more printer-friendly, refs added. v3: some typos corrected