Uplifting the Iwasawa

Franzen, Anne T.; Kaura, Payal; Misra, Aalok; Ray, Rajarshi

doi:10.1002/prop.200510269

Cited by 12 publications

(20 citation statements)

References 20 publications

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“…Then (7.12) implies that g is also constant and so it can be chosen as g = 1. In the gauge f = g = 1, one haŝ 27) which together with (7.15) imply that all the components ofΩ A,+B = 0. It is then easy to see that (7.12)-(7.17) imply that the remaining components of the connection one-form, Ω =Ω A e A , take values in g 2 .…”

Section: Holonomy Of∇ Connectionmentioning

confidence: 99%

“…Using similar arguments to those we have presented for the Spin(7) ⋉ R 8 case and introducing coordinates along the null Killing vector X = ∂ ∂u , we can write the spacetime metric in the gauge f = 1 as 27) where all the components are functions of v, y I and i X H = de − = dm. In addition the second equation in (6.12) implies that dm takes values in su(4) ⊕ s R 8 .…”

Section: Local Coordinates Distributions and A Deformation Familymentioning

confidence: 99%

“…More recently, these geometries with torsion have been studied using the Gray-Hervella classification techniques [22], see e.g. [23,24,25,26,27]. So far in the applications of these geometries in the context of tendimensional supergravity, it has been assumed that the spacetime is a product, R 9−n,1 × X n , and the non-trivial part of the geometry is that of the Riemannian manifold X n .…”

Section: Introductionmentioning

confidence: 99%

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The spinorial geometry of supersymmetric heterotic string backgrounds

Gran

Lohrmann

Papadopoulos

2006

J. High Energy Phys.

296

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We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection∇ with torsion H, the NS⊗NS three-form field strength, are Killing. We find that there are two classes of such backgrounds, the null and the timelike. The Killing spinors of the null backgrounds have stability subgroups K ⋉ R 8 in Spin(9, 1), for K = Spin(7), SU (4), Sp(2), SU (2)×SU (2) and {1}, and the Killing spinors of the timelike backgrounds have stability subgroups G 2 , SU (3), SU (2) and {1}. The former admit a single null∇-parallel vector field while the latter admit a timelike and two, three, five and nine spacelike∇-parallel vector fields, respectively. The spacetime of the null backgrounds is a Lorentzian two-parameter family of Riemannian manifolds B with skew-symmetric torsion. If the rotation of the null vector field vanishes, the holonomy of the connection with torsion of B is contained in K. The spacetime of time-like backgrounds is a principal bundle P with fibre a Lorentzian Lie group and base space a suitable Riemannian manifold with skew-symmetric torsion. The principal bundle is equipped with a connection λ which determines the non-horizontal part of the spacetime metric and of H. The curvature of λ takes values in an appropriate Lie algebra constructed from that of K. In addition dH has only horizontal components and contains the Pontrjagin class of P . We have computed in all cases the Killing spinor bilinears, expressed the fluxes in terms of the geometry and determine the field equations that are implied by the Killing spinor equations.

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Section: Holonomy Of∇ Connectionmentioning

confidence: 99%

Section: Local Coordinates Distributions and A Deformation Familymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The spinorial geometry of supersymmetric heterotic string backgrounds

Gran

Lohrmann

Papadopoulos

2006

J. High Energy Phys.

296

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“…Sixdimensional non-Kähler manifolds with SUm structure have been discussed in heterotic [26,47,48], types IIA [26 -30], and IIB [49][50][51][52] strings. Compactifications of M theory using G 2 structures and SUm structures [31][32][33][34][35][36][37][38][39] have also been studied.…”

Section: Reviewmentioning

confidence: 99%

AdS strings with torsion: Noncomplex heterotic compactifications

2005

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Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a tendimensional approach to find a new class of four-dimensional supersymmetric AdS 4 compactifications on almost-Hermitian manifolds of SU3 structure. Computation of the torsion allows a classification of the internal geometry, which for a particular combination of fluxes and condensate, is nearly Kähler. We argue that all moduli are fixed, and we show that the Kähler potential and superpotential proposed in the literature yield the correct AdS 4 radius. In the nearly Kähler case, we are able to solve the H Bianchi identity using a nonstandard embedding. Finally, we point out subtleties in deriving the effective superpotential and understanding the heterotic supergravity in the presence of a gaugino condensate.

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“…Perhaps the results presented in our work have applications related to these references, and also to Ref. [79].…”

Section: Acknowledgmentsmentioning

confidence: 82%

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

Santillán

2006

Phys. Rev. D

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It is found the most general local form of the 11-dimensional supergravity backgrounds which, by reduction along one isometry, gives rise to IIA supergravity solutions with a RR field and a nontrivial dilaton, and for which the condition F 1;1 0 holds.This condition is stronger than the usual condition F ab J ab 0, required by supersymmetry. It is shown that these D6 wrapped backgrounds arise from the direct sum of the flat Minkowski metric with certain G 2 holonomy metrics admitting an U1 action, with a local form found by Apostolov and Salamon. Indeed, the strong supersymmetry condition is equivalent to the statement that there is a new isometry on the G 2 manifold, which commutes with the old one; therefore these metrics are inherently toric. An example that is asymptotically Calabi-Yau metric is presented. We find other G 2 metrics which give rise to half-flat SU3 structures. All these examples possess an U1 U1 U1 isometry subgroup. Supergravity solutions without fluxes corresponding to these G 2 metrics are constructed. The presence of a T 3 subgroup of isometries permits to apply the -deformation technique in order to generate new supergravity solutions with fluxes.

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Uplifting the Iwasawa

Cited by 12 publications

References 20 publications

The spinorial geometry of supersymmetric heterotic string backgrounds

The spinorial geometry of supersymmetric heterotic string backgrounds

AdS strings with torsion: Noncomplex heterotic compactifications

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

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