New spin(7) holonomy metrics admitting G{sub 2} holonomy reductions and M-theory/type-IIA dualities
- Department of Mathematics University of Rochester, Rochester, New York, 14627 (United States)
- Hamilton Mathematics Institute and School of Mathematics Trinity College, Dublin 2 (Ireland)
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 instanton and, to the best of our knowledge, have not been previously considered in the literature.
- OSTI ID:
- 21308368
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 79, Issue 8; Other Information: DOI: 10.1103/PhysRevD.79.086009; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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