New spin(7) holonomy metrics admittingG2holonomy reductions and M-theory/type-IIA dualities

Abstract

As is well known, when D6 branes wrap a special Lagrangian cycle on a noncompact Calabi-Yau threefold in such a way that the internal string frame metric is a Kaehler one there exists a dual description, which is given in terms of a purely geometrical 11-dimensional background with an internal metric of G{sub 2} holonomy. It is also known that when D6 branes wrap a coassociative cycle of a noncompact G{sub 2} manifold in the presence of a self-dual two-form strength the internal part of the string frame metric is conformal to the G{sub 2} metric and there exists a dual description, which is expressed in terms of a purely geometrical 11-dimensional background with an internal noncompact metric of spin(7) holonomy. In the present work it is shown that any G{sub 2} metric participating in the first of these dualities necessarily participates in one of the second type. Additionally, several explicit spin(7) holonomy metrics admitting a G{sub 2} holonomy reduction along one isometry are constructed. These metrics can be described as R fibrations over a 6-dimensional Kaehler metric, thus realizing the pattern spin(7){yields}G{sub 2}{yields}(Kahler) mentioned above. Several of these examples are further described as fibrations over the Eguchi-Hanson gravitational instantonmore » and, to the best of our knowledge, have not been previously considered in the literature.« less