Six-Dimensional Nearly Kähler Manifolds of Cohomogeneity One (II)

Podestà, Fabio; Spiro, Andrea

doi:10.1007/s00220-012-1482-3

Cited by 14 publications

(18 citation statements)

References 28 publications

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“…Only very recently, a combination of G-structure methods [33] with a two-step reductionà la Maldacena-Núñez [20] has produced explicit, analytic, N = 1 warped product AdS 4 solutions in massive IIA with (typically, but not necessarily, hyperbolic) internal spaces with SU(3) × SU(3)-1 Only very recently, existence results of inhomogeneous nearly-Kähler metrics on S 6 and other manifolds have been given [28]. See also [29,30]. Analytic, closed form expressions for such metrics are not known.…”

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confidence: 99%

AdS4 solutions of massive IIA from dyonic ISO(7) supergravity

Varela

2016

J. High Energ. Phys.

101

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Explicit formulae are given for the consistent truncation of massive type IIA supergravity on the six-sphere to the SU(3)-invariant sector of D = 4 N = 8 supergravity with dyonic ISO(7) gauging. These formulae are then used to construct AdS 4 solutions of massive type IIA via uplift on S 6 of the critical points of the D = 4 supergravity with at least SU(3) symmetry. We find a new N = 1 solution with SU(3) symmetry, a new non-supersymmetric solution with SO(6) symmetry, and recover previously known solutions. We quantise the fluxes, calculate the gravitational free energies of the solutions and discuss the stability of the non-supersymmetric ones. Among these, a (previously known) G 2 -invariant solution is found to be stable. factor, these solutions are typically supported by internal values of the supergravity forms. The metrics on the internal S 7 and S 5 are usually inhomogeneous and display isometry groups smaller than SO(8) and SO(6). A two-step variant of this uplifting method was introduced in [20], where a spherical truncation to some intermediate dimension, e.g. D = 7 [21, 22], followed by a further reduction on a suitable (usually hyperbolic) space was performed to obtain supersymmetric AdS 4 or AdS 5 solutions.All of the above AdS 4 and AdS 5 direct product solutions and most (but not all, see e.g.[23]) of the warped products are partially supported by a non-vanishing ('electric') Freund-Rubin-like termF (4) ∼ vol(AdS) 4 in D = 11 andF (5) ∼ vol(AdS) 5 in type IIB. This reflects that the corresponding solutions describe conformal phases of the M2, D3 and, for [23], M5 brane field theories. Since type IIA supergravity also contains a four-form field strengthF 4 , it would be natural to expect that the above plethora of AdS 4 solutions in D = 11 had a counterpart in type IIA. However, this is not the case: excluding the massless IIA solutions obtained by circle reduction from D = 11, only a handful of AdS 4 solutions in type IIA are known, either smooth and sourcelss or singular and with sources. And most of them are only known numerically.Massive type IIA supergravity [24] does admit a direct product Freund-Rubin solution AdS 4 ×S 6 [24], where S 6 is equipped with the usual, round, homogeneous, SO(7)-symmetric metric: see equation (4.8). However, unlike its maximally supersymmetric counterparts in D = 11 [4] and type IIB [5], it breaks all supersymmetries. Furthermore, as it will be argued below, this solution is unstable. G-structure methods have been used to classify supersymmetric AdS 4 solutions in type IIA (as well as in other contexts) and, in some cases, these results have led to explicit classes of solutions. N = 1 AdS 4 solutions with SU(3)-structure were classified in [25] and [26]. An explicit class of N = 1 solutions of massive type IIA involving the direct product of AdS 4 with a nearly-Kähler six-dimensional manifold was discovered in [25]. This class includes, in particular, the homogeneous N = 1 direct product AdS 4 × S 6 , where the six-sphere is now regarded as S 6 = G 2 /SU(3) and ...

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confidence: 99%

AdS4 solutions of massive IIA from dyonic ISO(7) supergravity

Varela

2016

J. High Energ. Phys.

101

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“…In [15,16], Podestà and Spiro gave the list of all 6-dimensional manifolds of cohomogeneity 1 on which the existence of NK-structures of cohomogeneity 1 is possible.…”

Section: Manifolds Of Cohomogeneitymentioning

confidence: 99%

Quasi-Kähler Structures of Cohomogeneity 1 on $ S^{2}\times S^{4} $

Daurtseva

2020

Sib Math J

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“…We refer the reader to [1,14,17,18] for basic notions on cohomogeneity one isometric actions. Following the notation of [18], we consider the Lie algebra so(4) ∼ = su(2) + su(2) and we fix the following basis of su(2)…”

Section: Non-compact Cohomogeneity One Examplesmentioning

confidence: 99%

On the automorphism group of a symplectic half-flat 6-manifold

Podestà

Raffero

2018

Forum Mathematicum

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We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat SU(3)-structure has abelian Lie algebra with dimension bounded by min{5, b1(M )}. Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on T S 3 which are invariant under a cohomogeneity one action of SO(4).2010 Mathematics Subject Classification. 53C10, 57S15.

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Six-Dimensional Nearly Kähler Manifolds of Cohomogeneity One (II)

Cited by 14 publications

References 28 publications

AdS4 solutions of massive IIA from dyonic ISO(7) supergravity

AdS4 solutions of massive IIA from dyonic ISO(7) supergravity

Quasi-Kähler Structures of Cohomogeneity 1 on $ S^{2}\times S^{4} $

On the automorphism group of a symplectic half-flat 6-manifold

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