Warped generalized geometry compactifications, effective theories and non‐perturbative effects

Koerber, Paul; Martucci, Luca

doi:10.1002/prop.200810552

Cited by 16 publications

(55 citation statements)

References 37 publications

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“…Thus, at large distances the structure is approximately SU (3), but the presence of a small cosmological constant remains. This indicates that the description proposed in [23,24] in terms of smeared instantons can capture the important physics as seen from a distant observer. Also, the fact that µ and the deformation parameter ϕ are small far away from the region where NP effects are large could allow for a perturbative treatment.…”

Section: Further Commentsmentioning

confidence: 84%

“…We would also like to point out that a connection between the non-perturbatively modified supersymmetry equation (3.7) and a would-be ten-dimensional description of the supersymmetric AdS 4 solution of [1] was attempted in [23,24]. However, this was done by using smeared instatons, that is, roughly speaking, by replacing the NP current δ 2 [Σ 4 ] in (3.4) by a suitably normalized two-form proportional to Im Ψ 1 ∼ J, allowing the authors to keep the original SU (3) structure.…”

Section: Discussionmentioning

confidence: 99%

“…Given this superpotential, Refs [23,24] and [39] showed that the F-flatness and Dflatness conditions amount to the full supersymmetry conditions (2.6). For that, one has to perform a dimensional reduction, using the (string-frame) metric Ansatz (2.1).…”

Section: Ten-dimensional Perspectivementioning

confidence: 99%

“…Thus, this is not suited for deriving the complete ten dimensional supersymmetry conditions in more general compactifications. This puzzle was beautifully solved in a series of papers [23,24,28,30]. Keeping in mind the familiar expressions in backgrounds compatible with D5 and D6-branes…”

Section: Ten-dimensional Perspectivementioning

confidence: 99%

“…The first step towards answering the first of these questions was beautifully addressed by Koerber and Martucci in [23,24], using the framework of Generalized Complex Geometry (GCG; for a review, see [25]), which we shall use. They first showed (see also [26]) that the conditions for N = 1 supersymmetry (in the absence of condensates) [27] are equivalent to the F-and D-flatness conditions for the 10D off-shell superpotential [28][29][30] that generalizes the Gukov-Vafa-Witten superpotential [31] for 3-form fluxes on Calabi-Yau manifolds.…”

Section: Introductionmentioning

confidence: 99%

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Kähler moduli stabilization from ten dimensions

Bena

Graña

Kovensky

et al. 2019

J. High Energ. Phys.

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We describe the back-reaction of gaugino condensates in supersymmetric AdS 4 Type II String Theory compactifications with fluxes. We use generalized complex geometry to capture the modification of the ten-dimensional supersymmetry equations and show that the cosmological constant prevents the cycle wrapped by the branes with gaugino condensation from shrinking to zero size. Thus, unlike in ordinary geometric transitions in flat space, the volume of this cycle remains finite. For D7 branes with gaugino condensation, this gives a ten-dimensional account of Kähler moduli stabilization. Furthermore, by matching the ten-dimensional supergravity solutions near and far from the cycle wrapped by the D7 branes, we find a relation between the size of this cycle and the cosmological constant. This relation agrees with the supersymmetric AdS vacuum condition obtained by KKLT using effective field theory.

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Section: Further Commentsmentioning

confidence: 84%

Section: Discussionmentioning

confidence: 99%

Section: Ten-dimensional Perspectivementioning

confidence: 99%

Section: Ten-dimensional Perspectivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kähler moduli stabilization from ten dimensions

Bena

Graña

Kovensky

et al. 2019

J. High Energ. Phys.

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Generalized geometry and partial supersymmetry breaking

Triendl

2010

Fortschritte der Physik

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This review article consists of two parts. 1 In the first part we use the formalism of (exceptional) generalized geometry to derive the scalar field space of SU(2) × SU(2)-structure compactifications. We show that in contrast to SU(3)×SU(3) structures, there is no dynamical SU(2)×SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we derive the scalar manifold of the low-energy effective action for consistent Kaluza-Klein truncations as expected from N = 4 supergravity. In the second part we then determine the general conditions for the existence of stable Minkowski and AdS N = 1 vacua in spontaneously broken gauged N = 2 supergravities and construct the general solution under the assumption that two appropriate commuting isometries exist in the hypermultiplet sector. Furthermore, we derive the low-energy effective action below the scale of partial supersymmetry breaking and show that it satisfies the constraints of N = 1 supergravity. We then apply the discussion to special quaternionic-Kähler geometries which appear in the low-energy limit of SU(3) × SU(3)-structure compactifications and construct Killing vectors with the right properties. Finally we discuss the string theory realizations for these solutions.

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Generalising G2 geometry: involutivity, moment maps and moduli

Ashmore

Strickland‐Constable

Tennyson

et al. 2021

J. High Energ. Phys.

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We analyse the geometry of generic Minkowski $$ \mathcal{N} $$ N = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al. (GMPT). Using E7(7) × ℝ+ generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E7(7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.

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Warped generalized geometry compactifications, effective theories and non‐perturbative effects

Cited by 16 publications

References 37 publications

Kähler moduli stabilization from ten dimensions

Kähler moduli stabilization from ten dimensions

Generalized geometry and partial supersymmetry breaking

Generalising G2 geometry: involutivity, moment maps and moduli

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