On spin(7) holonomy metric based on SU(3) / U(1) - INSPIRE

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On spin(7) holonomy metric based on SU(3) / U(1)

Hiroaki Kanno
(
- Nagoya U.
)
,
Yukinori Yasui
(
- Osaka City U.
)

Aug, 2001

19 pages

Published in:

J.Geom.Phys. 43 (2002) 293-309

e-Print:

hep-th/0108226 [hep-th]

DOI:

10.1016/S0393-0440(02)00018-9

View in:

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Abstract:

We investigate the

Spin(7)

holonomy metric of cohomogeneity one with the principal orbit

SU(3)/U(1)

. A choice of U(1) in the two dimensional Cartan subalgebra is left as free and this allows manifest

\Sigma_3=W(SU(3))

(= the Weyl group) symmetric formulation. We find asymptotically locally conical (ALC) metrics as octonionic gravitational instantons. These ALC metrics have orbifold singularities in general, but a particular choice of the U(1) subgroup gives a new regular metric of

Spin(7)

holonomy. Complex projective space

{\bf CP}(2)

that is a supersymmetric four-cycle appears as a singular orbit. A perturbative analysis of the solution near the singular orbit shows an evidence of a more general family of ALC solutions. The global topology of the manifold depends on a choice of the U(1) subgroup. We also obtain an

L^2

-normalisable harmonic 4-form in the background of the ALC metric.

holonomy: Spin(7)
orbit: SU(3)/U(1)
symmetry: Weyl
differential forms: harmonic
singularity
instanton
octonion
topology

References(21)

Figures(0)

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