New complete noncompact Spin(7) manifolds

By M. Cvetič, G. W. Gibbons, Hong Lu, C. N. Pope. 2001

133 citations recorded by the source corpus.

Abstract We construct new explicit metrics on complete noncompact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by A 8 , is topologically R 8 and another, which we denote by B 8 , is the bundle of chiral spinors over S4. Unlike the previously-known complete noncompact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S4, our new 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 CP 3 . We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L2-normalisable harmonic 4-form for the A 8 manifold, and two such 4-forms (of opposite dualities) for the B 8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A 8 and B 8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In Appendix A we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B 8 + and B 8 − similar to B 8 .

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d0b6da5b68385aeb85e72777cb6298fee724f556

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Citations in the corpus

Gauge theory at large N and new G2 holonomy metrics (2001, unknown): “June 2001”
Some New Examples of Non-K\"ahler Ricci Solitons (2008, background): “ viewed as the Ricci soliton analogues of the Asymptotically Conical (AC) and Asymptotically Locally Conical (ALC) conditions satisﬁed by many of the known complete non-compact Ricci-ﬂat metrics (see [CGLP] for example). 4. Analysing the ﬂow To check smoothness at the collapsing submanifold, we must”
M-theory pp-waves, Penrose limits and supernumerary supersymmetries (2002, background): “. It can be lifted to M-theory, where it acquires an interpretation as a supersymmetric deformed M2-brane, i.e. an M2-brane in which an additional 4-form ﬂux is turned on in the transverse space [22]-[28]. An intriguing feature of the deformed M2-branes obtained by this T-dualisation procedure is th”
M theory and singularities of exceptional holonomy manifolds (2004, unknown): “Again, this method can be used to obtain the asymptotically conical metrics listed in Table 4, as well as other Spin(7) metrics recently found in [35, 36, 25, 37].”