New Spin(7) holonomy metrics admiting G2 holonomy reductions and M-theory/IIA dualities

S. Salur; O. Santillan

doi:10.1103/PhysRevD.79.086009

paper

New Spin(7) holonomy metrics admiting G2 holonomy reductions and M-theory/IIA dualities

arXiv:0811.4422 · doi:10.1103/PhysRevD.79.086009

Abstract

IAs is well known, when D6 branes wrap a special lagrangian cycle on a non compact CY 3-fold in such a way that the internal string frame metric is Kahler there exists a dual description, which is given in terms of a purely geometrical eleven dimensional background with an internal metric of $G_{2}$ holonomy. It is also known that when D6 branes wrap a coassociative cycle of a non compact $G_{2}$ manifold in presence of a self-dual two form strength the internal part of the string frame metric is conformal to the $G_{2}$ metric and there exists a dual description, which is expressed in terms of a purely geometrical eleven dimensional background with an internal non compact metric of Spin(7) holonomy. In the present work it is shown that any $G_{2}$ 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 $G_{2}$ holonomy reduction along one isometry are constructed. These metrics can be described as $R$ -fibrations over a 6-dimensional Kahler metric, thus realizing the pattern Spin(7) $\to G_{2} \to$ (Kahler) mentioned above. Several of these examples are further described as fibrations over the Eguchi-Hanson gravitational instanton and, to the best of our knowledge, have not been previously considered in the literature.

Final version, accepted in Phys.Rev.D

New Spin(7) holonomy metrics admiting G2 holonomy reductions and M-theory/IIA dualities

Abstract

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