On Spin(7) holonomy metric based on SU(3)/U(1)
نویسندگان
چکیده
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 Σ3 = W (SU(3)) (= the Weyl group) symmetric formulation. We find asymptotically locally conical (ALC) metrics as octonionic gravitational instantons. Complex projective space CP(2) that is a supersymmetric four-cycle appears as a singular orbit and we make a perturbative analysis of the solution near the singular orbit. The global topology of the manifold depends on a choice of the U(1) subgroup. We also obtain an L2-normalisable harmonic 4-form in the background of the ALC metric. e-mail: [email protected] e-mail: [email protected]
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On Spin(7) holonomy metric based on SU(3)/U(1) : II
We continue the investigation of Spin(7) holonomy metric of cohomogeneity one with the principal orbit SU(3)/U(1). A special choice of U(1) embedding in SU(3) allows more general metric ansatz with five metric functions. There are two possible singular orbits in the first order system of Spin(7) instanton equation. One is the flag manifold SU(3)/T 2 also known as the twister space of CP(2) and ...
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