7-Dimensional compact Riemannian manifolds with Killing spinors

Friedrich, Thomas; Kath, Ines

doi:10.1007/bf02097009

Cited by 72 publications

(61 citation statements)

References 31 publications

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“…In the regular case this goes back to a construction of Kobayashi [Kob2] together with Hatakeyama [Hat]. There is also a description in the context of Sasakian-Einstein geometry in [FrKat2,BFGK] …”

Section: (Iv) (S G) Is Sasakian-einstein If and Only If (Z H) Is Kämentioning

confidence: 98%

On Sasakian–einstein Geometry

2000

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We introduce a multiplication ⋆ (we call it a join) on the space of all compact Sasakian-Einstein orbifolds [Formula: see text] and show that [Formula: see text] has the structure of a commutative associative topological monoid. The set [Formula: see text] of all compact regular Sasakian–Einstein manifolds is then a submonoid. The set of smooth manifolds in [Formula: see text] is not closed under this multiplication; however, the join [Formula: see text] of two Sasakian–Einstein manifolds is smooth under some additional conditions which we specify. We use this construction to obtain many old and new examples of Sasakain–Einstein manifolds. In particular, in every odd dimension greater that five we obtain spaces with arbitrary second Betti number.

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Section: (Iv) (S G) Is Sasakian-einstein If and Only If (Z H) Is Kämentioning

confidence: 98%

On Sasakian–einstein Geometry

2000

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“…Examples of spaces Y 7 satisfying the requirements of the previous section are some regular An exhaustive list is given by [40]:…”

Section: Examplesmentioning

confidence: 99%

Membranes with topological charge andAdS4/CFT3correspondence

Klebanov¹,

Pufu²,

Teşileanu³

2010

Phys. Rev. D

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If the second Betti number b 2 of a Sasaki-Einstein manifold Y 7 does not vanish, then M-theory on AdS 4 × Y 7 possesses "topological" U (1) b 2 gauge symmetry. The corresponding Abelian gauge fields come from three-form fluctuations with one index in AdS 4 and the other two in Y 7 . We find black membrane solutions carrying one of these U (1) charges. In the zero temperature limit, our solutions interpolate between AdS 4 × Y 7 in the UV andbackground is by itself a solution of the supergravity equations of motion. These solutions do not appear to preserve any supersymmetry. We search for their possible instabilities and do not find any. We also discuss the meaning of our charged membrane backgrounds in a dual quiver ChernSimons gauge theory with a global U (1) charge density. Finally, we present a simple analytic solution which has the same IR but different UV behavior. We reduce this solution to type IIA string theory, and perform T-duality to type IIB. The type IIB metric turns out to be a product of the squashed Y 7 and the extremal BTZ black hole. We discuss an interpretation of this type IIB background in terms of the (1 + 1)-dimensional CFT on D3-branes partially wrapped over the squashed Y

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“…(3.10), the internal space has to be an Einstein space and can be lifted to an 8-d space of special holonomy. There are three cases of special interest, which have been also discussed in the mathematical literature [41,42,43]; these three classes are related to the number of real internal spinors. If there is a single internal spinor, the 7-d space has G 2 structures and can be lifted to an 8-d space of Spin (7) holonomy; for two real spinor we have SU(3) structures and the lift yields a space of SU(4) holonomy (Calabi-Yau); finally the case with three real spinors can be lifted to an 8-d hyper Kähler space.…”

Section: Supersymmetry Variationsmentioning

confidence: 99%

Classification of supersymmetric flux vacua in M-theory

2006

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We present a comprehensive classification of supersymmetric vacua of M-theory compactification on seven-dimensional manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have N = 1,2,3,4 supersymmetry and the internal space allows for SU (2), SU (3) or G 2 structures. In particular, we find for N = 2 supersymmetry, that the external space-time is Minkowski and the base manifold of the internal space is conformally Kähler for SU (2) structures, while for SU (3) structures the internal space has to be EinsteinSasaki and no internal fluxes are allowed. Moreover, we provide a new vacuum with N = 1 supersymmetry and SU (3) structure, where all fluxes are non-zero and the first order differential equations are solved.

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7-Dimensional compact Riemannian manifolds with Killing spinors

Cited by 72 publications

References 31 publications

On Sasakian–einstein Geometry

On Sasakian–einstein Geometry

Membranes with topological charge andAdS4/CFT3correspondence

Classification of supersymmetric flux vacua in M-theory

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