D-branes in nongeometric backgrounds

Lawrence, Albion; Schulz, Michael B.; Wecht, Brian

doi:10.1088/1126-6708/2006/07/038

Cited by 51 publications

(98 citation statements)

References 88 publications

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“…The complex dilaton is instead 26) where C 0 is the R-R 0-form. The Kähler moduli can be extracted from the complexified 4-form 27) where C 4 is the RR 4-form.…”

Section: Iib Orientifold With O3-planesmentioning

confidence: 99%

More dual fluxes and moduli fixing

Aldazábal¹,

Cámara²,

Font³

et al. 2006

J. High Energy Phys.

181

508

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We generalize the recent proposal that invariance under T-duality leads to additional nongeometric fluxes required so that superpotentials in type IIA and type IIB orientifolds match.We show that invariance under type IIB S-duality requires the introduction of a new set of fluxes leading to further superpotential terms. We find new classes of N =1 supersymmetric Minkowski vacua based on type IIB toroidal orientifolds in which not only dilaton and complex moduli but also Kähler moduli are fixed. The chains of dualities relating type II orientifolds to heterotic and M-theory compactifications suggests the existence of yet further flux degrees of freedom. Restricting to a particular type IIA/IIB or heterotic compactification only some of these degrees of freedom have a simple perturbative and/or geometric interpretation.

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“…The complex dilaton is instead 26) where C 0 is the R-R 0-form. The Kähler moduli can be extracted from the complexified 4-form 27) where C 4 is the RR 4-form.…”

Section: Iib Orientifold With O3-planesmentioning

confidence: 99%

More dual fluxes and moduli fixing

Aldazábal¹,

Cámara²,

Font³

et al. 2006

J. High Energy Phys.

181

508

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“…One should however be careful when making such a claim because, as we have seen during our discussion, the interplay between D-branes and fluxes is non-trivial and, in general, the inclusion of background fluxes modifies the D-brane spectrum of a compactification. How this works for non-geometric vacua is still not known, since we do not have a full understanding of the D-brane spectrum in this case (see [42,116,148] for some results on this problem). We can however learn some lesson from the effects of geometric fluxes described above.…”

Section: Non-geometric Backgroundsmentioning

confidence: 99%

Progress in D‐brane model building

Marchesano¹

2007

Fortschritte der Physik

154

234

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The state of the art in D-brane model building is briefly reviewed, focusing on recent achievements in the construction of D = 4 N = 1 type II string vacua with semi-realistic gauge sectors. Such progress relies on a better understanding of the spectrum of BPS D-branes, the effective field theory obtained from them and the explicit construction of vacua. We first consider D-branes in standard Calabi-Yau compactifications, and then the more involved case of compactifications with fluxes. We discuss how the non-trivial interplay between D-branes and fluxes modifies the previous model-building rules, as well as provides new possibilities to connect string theory to particle physics. MotivationAs often emphasized in the literature, string theory gained its popularity among physicists in the mid-80's, as it was recognized as an outstanding candidate for a unified theory of all forces in nature. Not only would it incorporate quantum gravity, but also supersymmetry and non-Abelian gauge interactions. With such ingredients it was soon realized that, upon compactification, one could conceive D = 4 N = 1 effective theories remarkably close to natural extensions of the Standard Model [1].Further developments of the theory showed that the set of string theory vacua is quite complex even at a qualitative level. On the one hand we learned that seemingly different vacua could be dual to each other and, in fact, should be considered to be the same. On the other hand, it has been estimated that the set of semi-realistic vacua is enormous. This latter point has recently raised the question of whether string theory can reproduce almost any D = 4 effective theory that one may think of and, in particular, many possible physics beyond the Standard Model. If that was the case, one may drop the classical strategy to focus on a particular string theory model by means of some vacuum selection principle, and instead try to extract physical information out of the ensemble of realistic vacua via an statistical approach [2]. Now, while string theory has proven to be an excellent generator of phenomenologically interesting scenarios, a string vacuum reproducing the physics observed at particle accelerators is yet to be found. Individual vacua analyzed so far not only fail to describe fully realistic D = 4 physics because of some technical details like extra massless particles or unrealistic couplings, but also because of deep conceptual issues like gauge coupling unification, hierarchy problems and supersymmetry breaking. Moreover, recent cosmological observations have slightly changed our perspective on how a semi-realistic vacuum should be obtained and, in general, agreement with cosmological data puts even more constraints on realistic string constructions.Pointing out these facts is not intended to discourage those interested in the field of model building. On the contrary, there has recently been huge progress (some of which the present review is based on) in constructing vacua which are more and more realistic, and we expect much more p...

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“…The T-dualized directions are doubled, and T-duality transformations may patch the doubled fibres together. A sigma model with a T-fold as its target space was proposed, and its boundary conditions were studied in [14,15,16,17,18].(III) G × G structure compactifications: SU(3) × SU(3) structure manifolds are characterized in terms of a pair of pure spinors, constructed as bilinear combinations of a pair SU(3)-invariant spinors of Cliff(6). In case the SU(3)-invariant spinors are not parallel to each other, their linear independence is encoded by a non-vanishing one-form, and the discrepancy between left-and right-moving complex structures is a potential source of non-geometry and/or non-commutativity.…”

mentioning

confidence: 99%

T-duality with H-flux: Non-commutativity, T-folds and structure

Grange

Schäfer‐Nameki

2007

Nuclear Physics B

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Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The noncommutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) × SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors. IntroductionCompactifications with H-flux are known to give rise to topology changes and even to nongeometric situations when T-duality is performed along directions which have non-trivial support of the NSNS H-flux [1,2,3,4,5,6,7,8]. Non-geometry occurs for example in the very simple situation of a three-torus endowed with an H-flux proportional to its volume form. Consider namely the three-torus as a trivial T 2 -fibration over a circle. Upon T-duality along the fibre, the metric picks up a factor that makes it shrink under monodromy around the base circle. The monodromy around the base is a non-trivial element of the O(2, 2; Z) group acting on the two-torus. This prevents a three-dimensional global Riemannian description from existing. Further T-dualizing along the base leads to more pathological situations, where points do not exist even in a local coordinate patch, and the fibres are conjectured to become non-associative [9,10]. We will restrict ourselves to the case of two T-dualities, and assume that local coordinate patches do exist. Progress in the description of non-associative T-duals was achieved in the recent paper [11], which also contains observations on the open-string metric and non-commutativity for two T-dualities that have some overlap with ours.Essentially three conjectures have been put forward for the description of the T-dual of a torus with H-flux: 1 (I) Field of non-commutative tori: Mathai and Rosenberg proposed that T-dualizing along a two-torus with non-zero H-flux yields a fibration by (or more precisely: field of) noncommutative tori. In particular, this fibration is encoded in a closed one-form, which is obtained by integrating the NSNS flux along the fibre directions [7,12,13].(II) T-folds: these are spaces where T-dualities can act as transition functions between local patches [8]. The T-dualized directions are doubled, and T-duality transformations may patch the doubled fibres together. A sigma model with a T-fold as its target space was proposed, and its boundary conditions were studied in [14,15,16,17,18].(III) G × G struc...

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D-branes in nongeometric backgrounds

Cited by 51 publications

References 88 publications

More dual fluxes and moduli fixing

More dual fluxes and moduli fixing

Progress in D‐brane model building

T-duality with H-flux: Non-commutativity, T-folds and structure

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