RETRACTED: Cohomogeneity One Manifolds of Spin(7) and G2 Holonomy

Cvetič, Mirjam; Gibbons, G. W.; Lu, Hongxia; Pope, C.N.

doi:10.1006/aphy.2002.6289

Cited by 87 publications

(338 citation statements)

References 27 publications

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“…One can check that the equations are a consistent truncation of the second-order Einstein equations for the more general nine-function ansatz that was given in [14]. It should be emphasised that although the equations here have reduced to a four-function first-order system, the ansatz is inequivalent to the four-function ansatz introduced in [13].…”

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confidence: 89%

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M-Theory Conifolds

et al. 2002

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Seven-manifolds of G 2 holonomy provide a bridge between M-theory and string theory, via Kaluza-Klein reduction to Calabi-Yau six-manifolds. We find first-order equations for a new family of G 2 metrics D 7 , with S 3 × S 3 principal orbits. These are related at weak string coupling to the resolved conifold, paralleling earlier examples B 7 that are related to the deformed conifold, allowing a deeper study of topology change and mirror symmetry in M-theory. The D 7 metrics' non-trivial parameter characterises the squashing of an S 3 bolt, which limits to S 2 at weak coupling. In general the D 7 metrics are asymptotically locally conical, with a nowhere-singular circle action.

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confidence: 89%

“…The associated Calabi-Yau space is the Ricci-flat Kähler metric on a complex line bundle over S 2 × S 2 [11,12]. Other work has provided G 2 metrics B 7 associated with the deformed conifold Calabi-Yau space [13,14]. However, in this case the radius R vanishes on an S 3 supersymmetric (calibrated) cycle in the interior.…”

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confidence: 99%

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“…However, we shall argue below that this is not the case. The second conical singularity discussed in the literature corresponds to a cone over SU(3)/U(1) [11,12,13]. It is in this case that we suggest an interesting phase transition.…”

Section: Topologymentioning

confidence: 54%

Conifold transitions and five-brane condensation in M-theory onSpin(7) manifolds

Gukov

Sparks

Tong

2003

Class. Quantum Grav.

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We conjecture a topology changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a CP 2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S 5 . Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G 2 holonomy manifold with either wrapped D6-branes, or background Ramond-Ramond flux. This is the first nontrivial example of a topology changing transition with only 1/16 supersymmetry.

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“…The corresponding metric is ALC because c(r) remains finite at infinity. It was shown [10,9] that this solution extends to a two parameter family of solutions, B 7 , that are not known explicitly. A limiting case of this family is the AC solution which is known exactly 1…”

Section: Introductionmentioning

confidence: 89%

“…The Taylor expansions of the radial functions about the origin, to the order that we need them, are for B 7 [9]:…”

Section: B 7 and Cmentioning

confidence: 99%

Axisymmetric non-abelian BPS monopoles from G2 metrics

Hartnoll¹

2002

Nuclear Physics B

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Exact SU (2) × U (1) self-gravitating BPS global monopoles in four dimensions are constructed by dimensional reduction of eight dimensional metrics with G 2 holonomy asymptotic to cones over S 3 × S 3 . The solutions carry two topological charges in an interesting way. They are generically axially but not spherically symmetric. This last fact is related to the isometries and asymptotic topology of the G 2 metrics. It is further shown that some G 2 metrics known numerically reduce to supersymmetric cosmic strings.

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RETRACTED: Cohomogeneity One Manifolds of Spin(7) and G2 Holonomy

Cited by 87 publications

References 27 publications

M-Theory Conifolds

M-Theory Conifolds

Conifold transitions and five-brane condensation in M-theory onSpin(7) manifolds

Axisymmetric non-abelian BPS monopoles from G2 metrics

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