We show how certain diffeomorphism-invariant functionals on differential forms in dimensions 6, 7 and 8 generate in a natural way special geometrical structures in these dimensions: metrics of holonomy G2 and Spin(7), metrics with weak holonomy SU(3) and G2, and a new and unexplored example in dimension 8. The general formalism becomes a practical tool for calculating homogeneous or cohomogenei...

We review the relations between a family of domain-wall solutions to M-theory and gravitational instantons with special holonomy. When oxidized into the maximal-dimension parent supergravity, the transverse spaces of these domain walls become cohomogeneity-one spaces with generalized Heisenberg symmetries and a homoth-etic conformal symmetry. These metrics may also be obtained as scaling limits...

First, a word from our sponsor (particle physics). The mathematical reader should not expect to understand the physics, but (paraphrasing A. N. Varchenko) just let the words wash over you like music. Acharya & Witten [1] and Atiyah & Witten [2] have demonstrated that singularities in G2 holonomy manifolds 1 can compactify M -theory yielding effective quantum field theories in 3+1 dimensional Mi...

Abstract We conclude the classification of cohomogeneity one actions on symmetric spaces rank by classifying quaternionic hyperbolic up to orbit equivalence. As a by-product our proof, we produce uncountably many examples inhomogeneous isoparametric families hypersurfaces with constant principal curvatures in spaces.

At the leading order, the low-energy effective field equations in string theory admit solutions of the form of products of Minkowski spacetime and a Ricci-flat Calabi-Yau space. The equations of motion receive corrections at higher orders in α′, which imply that the Ricci-flat Calabi-Yau space is modified. In an appropriate choice of scheme, the Calabi-Yau space remains Kähler, but is no longer...