TASI lectures: special holonomy in string theory and M-theory
Steven S. Gubser
Abstract
A brief, example-oriented introduction is given to special holonomy and its uses in string theory and M-theory. We discuss Ak singularities and their resolution; the construction of a K3 surface by resolving T4/Z2; 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; G2 holonomy and its relation to N=1 supersymmetric compactifications of M-theory; certain isolated G2 singularities and their resolution; the Joyce construction of compact manifolds of G2 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.
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