New<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>holonomy metrics, D6 branes with inherent<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>×</mml:mo><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>isometry,

Santillán, Osvaldo P.

doi:10.1103/physrevd.73.126011

Cited by 4 publications

(4 citation statements)

References 87 publications

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“…Contracting (3.25) with w and using that the metric g 8 is S 1 -invariant we obtain 27) which implies…”

Section: Jhep05(2015)085mentioning

confidence: 84%

“…For instance, in reference [24] it was shown that a configuration of D6-branes wrapping a special Lagrangian cycle of a non-compact Calabi-Yau manifold such that the internal string frame metric is Kähler, is dual to a purely geometrical background in eleven dimensions with an internal metric of G 2 -holonomy. Other examples of torsion-free structures dual to configuration with fluxes, in other words, non-zero torsion, can be found in references [25][26][27][28], this time from six-dimensions to a G 2 -holonomy. For further examples and results in the Spin(7) and G 2 cases see reference [29,30].…”

Section: Jhep05(2015)085mentioning

confidence: 99%

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M-theory moduli spaces and torsion-free structures

Graña

Shahbazi

2015

J. High Energ. Phys.

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Motivated by the description of N = 1 M-theory compactifications to fourdimensions given by Exceptional Generalized Geometry, we propose a way to geometrize the M-theory fluxes by appropriately relating the compactification space to a higherdimensional manifold equipped with a torsion-free structure. As a non-trivial example of this proposal, we construct a bijection from the set of Spin(7)-structures on an eightdimensional S 1 -bundle to the set of G 2 -structures on the base space, fully characterizing the G 2 -torsion clases when the total space is equipped with a torsion-free Spin(7)-structure. Finally, we elaborate on how the higher-dimensional manifold and its moduli space of torsion-free structures can be used to obtain information about the moduli space of Mtheory compactifications.

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“…Contracting (3.25) with w and using that the metric g 8 is S 1 -invariant we obtain 27) which implies…”

Section: Jhep05(2015)085mentioning

confidence: 84%

Section: Jhep05(2015)085mentioning

confidence: 99%

M-theory moduli spaces and torsion-free structures

Graña

Shahbazi

2015

J. High Energ. Phys.

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“…One is that κ = α, in which case the solution is completely determined by one basic equation for G, given by (36). The other is that κ = 0, in which case the solution is completely determined by the basic equation (46).…”

Section: Case Ii: κ 1 =mentioning

confidence: 99%

“…Examples of complete metrics on non-compact manifolds in higher dimensions with G 2 and spin (7) holonomy were constructed in the later 1980s [16][17][18][19]. Inspired by the AdS/CFT correspondence and applications in M-theory compactification, large classes of explicit metrics on G 2 and spin (7) holonomy spaces have been constructed and their applications in string and M-theory have been discussed [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Constructing Calabi–Yau metrics from hyperkähler spaces

Lü¹,

Pang²,

Wang³

2010

Class. Quantum Grav.

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Recently, a metric construction for the Calabi-Yau 3-folds from a four-dimensional hyperkähler space by adding a complex line bundle was proposed. We extend the construction by adding a U (1) factor to the holomorphic (3, 0)-form, and obtain the explicit formalism for a generic hyperkähler base. We find that a discrete choice arises: the U (1) factor can either depend solely on the fibre coordinates or vanish. In each case, the metric is determined by one differential equation for the modified Kähler potential. As explicit examples, we obtain the generalized resolutions (up to orbifold singularity) of the cone of the Einstein-Sasaki spaces Y p,q . We also obtain a large class of new singular CY3 metrics with SU (2) × U (1) or SU (2) × U (1) 2 isometries.

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Toric G 2 and Spin(7) Holonomy Spaces from Gravitational Instantons and Other Examples

Giribet

Santillán

2007

Commun. Math. Phys.

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Non-compact G 2 holonomy metrics that arise from a T 2 bundle over a hyper-Kähler space are constructed. These are one parameter deformations of certain metrics studied by Gibbons, Lü, Pope and Stelle in [1]. Seven-dimensional spaces with G 2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational instantons are found, together with other examples. By using the Apostolov-Salamon theorem [2], we construct a new example that, still being a T 2 bundle over hyper-Kähler, represents a non trivial two parameter deformation of the metrics studied in [1]. We then review the Spin(7) metrics arising from a T 3 bundle over a hyper-Kähler and we find two parameter deformation of such spaces as well. We show that if the hyper-Kähler base satisfies certain properties, a non trivial three parameter deformations is also possible. The relation between these spaces with half-flat and almost G 2 holonomy structures is briefly discussed.The problem of classifying spaces of G 2 holonomy possessing one isometry whose Killing vector orbits form a Kähler six-dimensional space was analyzed both by physicist and mathematicians. In Ref. [23], it was concluded that such geometries are described by a sort of holomorphic monopole equation together with a condition related to the integrability of the complex structure. Such condition turns out to be stronger than the one required by supersymmetry. On the other hand, Apostolov and Salamon have proven in [2] that the Kähler condition yields the existence of a new Killing vector that commutes with the first, so that these metrics are toric. Besides, it was shown that such a G 2 metric yields a four-dimensional manifold equipped with a complex symplectic structure and a one-parameter family of functions and 2forms linked by second order equations (henceforth called Apostolov-Salamon equation). The inverse problem, i.e. the one of constructing a torsion-free G 2 structure starting from such a four-dimensional space was also discussed in [2]. Then, a natural question arises as to whether both description of this classification problem are equivalent. In Ref [24], it was argued that this is indeed the case. Moreover, in Ref. [1,2,24] such a construction was employed to generate new G 2 -metrics. In the present work, the solution generating technique will be analyzed in detail and a wider family of G 2 -metrics will be written down. In particular, the Eguchi-Hanson and the Taub-Nut metrics will be dimensionally extended to new examples of G 2 holonomy following the construction proposed in [1]. In section 2 we discuss the Apostolov-Salamon theorem [2], which formalizes a method for systematically constructing spaces with special holonomy G 2 by starting with a hyper-Kähler space in four-dimensions. This construction is actually the one previously employed by Gibbons, Lü, Pope and Stelle in Ref.[1] and here we discuss it within the framework of [2]. Then, we describe some explicit examples in order to illustrate the procedure. In particular, we show how some of the G 2 metrics obtained i...

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NewG2holonomy metrics, D6 branes with inherentU(1)×U(1)isometry,

Cited by 4 publications

References 87 publications

M-theory moduli spaces and torsion-free structures

M-theory moduli spaces and torsion-free structures

Constructing Calabi–Yau metrics from hyperkähler spaces

Toric G 2 and Spin(7) Holonomy Spaces from Gravitational Instantons and Other Examples

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