TASI lectures: special holonomy in string theory and M-theory

Abstract

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

References in corpus (14)

• M-Theory on Eight-Manifolds
• Superstrings and Topological Strings at Large N
• Three-Family Supersymmetric Standard-like Models from Intersecting Brane Worlds
• String Theory on Calabi-Yau Manifolds
• Chiral Fermions from Manifolds of $G_2$ Holonomy
• The geometry of three-forms in six and seven dimensions
• Gauge Theory at Large N and New G_2 Holonomy Metrics
• Superpotentials and Membrane Instantons
• On Realising N=1 Super Yang-Mills in M theory
• M-theory on Manifolds of G_2 Holonomy and Type IIA Orientifolds
• Supersymmetric Non-singular Fractional D2-branes and NS-NS 2-branes
• G(2) Holonomy Spaces from Invariant Three-Forms
• Compactifying M-Theory to Four Dimensions
• Lectures on special Lagrangian geometry

Cited by in corpus (6)

• Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
• Weyl doubling
• Hypercharge flux in F-theory and the stable Sen limit
• Toric G_2 and Spin(7) holonomy spaces from gravitational instantons and other examples
• Higher-dimensional field theories from type II supergravity
• Dirac equation on a G_2 manifold