Institution: | a Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA b DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, UK c Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109, USA d Department of Physics, Center for Theoretical Physics, Texas A&M University, College Station, TX 77843-4242, USA |
Abstract: | We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by
, is complete and non-singular on
. The other complete metrics are defined on manifolds with the topology of the bundle of chiral spinors over S4, and are denoted by
,
and
. The metrics on
and
occur in families with a non-trivial parameter. The metric on
arises for a limiting value of this parameter, and locally this metric is the same as the one for
. The new Spin(7) metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on
. We construct the covariantly constant spinor and calibrating 4-form. We also obtain an L2-normalisable harmonic 4-form for the
manifold, and two such 4-forms (of opposite dualities) for the
manifold. |