Complex/Symplectic Mirrors

Chuang, Wu-yen; Kachru, Shamit; Tomasiello, Alessandro

doi:10.1007/s00220-007-0262-y

Cited by 15 publications

(19 citation statements)

References 36 publications

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“…It then follows that the set of forms {α tor β } and {ω tor,α } constructed in this way satisfy relations equivalent to (C.7) and (C.8), namely [54] More importantly, this means that the phases (C.2) that these forms associate to each torsional 2 and 3-cycle of our construction are exactly the same as the bump forms δ α 4 and δ 3,β and, in this sense, they can be thought as the same elements of Tor H 4 (M 6 , Z) and Tor H 3 (M 6 , Z).…”

Section: D-branes and Torsion Invariantsmentioning

confidence: 95%

“…Constructing such torsional analogues of harmonic forms is quite similar to finding an appropriate basis of p-forms to perform dimensional reduction on SU(3)-structure manifolds [54,[60][61][62], since both problems deal with p-forms that are invisible to de Rham cohomology and correspond to the internal profile of massive 4d modes. with ω tor r−1 a globally well-defined (r − 1)-form, and k ∈ Z such that kα tor r is trivial also in Tor H r (M D , Z).…”

Section: Massive Rr U(1)'s From Torsionmentioning

confidence: 99%

“…How can we construct a smoothed out version of our bump functions? One possible way is, following [54], to consider objects in relative cohomology. Indeed, let us take a set of torsional 2-cycles {π tor 2,α } and 3-cycles {π tor,α 3…”

Section: D-branes and Torsion Invariantsmentioning

confidence: 99%

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RR photons

Cámara

Ibáñez

Marchesano

2011

J. High Energ. Phys.

163

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Type II string compactifications to 4d generically contain massless RamondRamond U(1) gauge symmetries. However there is no massless matter charged under these U(1)'s, which makes a priori difficult to measure any physical consequences of their existence. There is however a window of opportunity if these RR U(1)'s mix with the hypercharge U(1) Y (hence with the photon). In this paper we study in detail different avenues by which U(1) RR bosons may mix with D-brane U(1)'s. We concentrate on Type IIA orientifolds and their M-theory lift, and provide geometric criteria for the existence of such mixing, which may occur either via standard kinetic mixing or via the mass terms induced by Stückelberg couplings. The latter case is particularly interesting, and appears whenever D-branes wrap torsional p-cycles in the compactification manifold. We also show that in the presence of torsional cycles discrete gauge symmetries and Aharanov-Bohm strings and particles appear in the 4d effective action, and that type IIA Stückelberg couplings can be understood in terms of torsional (co)homology in M-theory. We provide examples of Type IIA Calabi-Yau orientifolds in which the required torsional cycles exist and kinetic mixing induced by mass mixing is present. We discuss some phenomenological consequences of our findings. In particular, we find that mass mixing may induce corrections relevant for hypercharge gauge coupling unification in F-theory SU(5) GUT's.

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Section: D-branes and Torsion Invariantsmentioning

confidence: 95%

Section: Massive Rr U(1)'s From Torsionmentioning

confidence: 99%

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RR photons

Cámara

Ibáñez

Marchesano

2011

J. High Energ. Phys.

163

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“…In a different context, it was also shown that IIA vacua should always be symplectic, whereas IIB vacua should be complex [92]. Mirror symmetry between complex and symplectic manifolds has been discussed in [98].…”

Section: Discussionmentioning

confidence: 99%

Geometric transitions on non‐Kähler manifolds

Knauf

2006

Fortschritte der Physik

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This article is based on the publications [1,2,3] and the author's PhD-thesis. We study geometric transitions on the supergravity level using the basic idea of [1], where a pair of nonKähler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup as suggested in [3]. The non-Kähler backgrounds we obtain in type IIA are non-trivially fibered due to their construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate that these non-Kähler manifolds are not half-flat and show that a symplectic structure exists on them at least locally. We also review the construction of new non-Kähler backgrounds in type I and heterotic theory as proposed in [2]. They are found by a series of T-and S-duality and can be argued to be related by geometric transitions as well. A local toy model is provided that fulfills the flux equations of motion in IIB and the torsional relation in heterotic theory, and that is consistent with the U-duality relating both theories. For the heterotic theory we also propose a global solution that fulfills the torsional relation because it is similar to the Maldacena-Nunez background.

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“…This is the underlying idea of compactifications on SU (3)×SU (3) structure manifolds. Such compactifications have been extensively studied in [6,8,7,[9][10][11][12][13][14][15][16][17][18]. Interestingly, the latter show a natural connection to Hitchin's generalized geometry [19,20], where in this picture SU (3)×SU (3) appears as the structure group of the generalized tangent bundle T M 6 ⊕ T * M 6 of the internal manifold M 6 .…”

Section: Introductionmentioning

confidence: 99%

Dimensional reductions of DFT and mirror symmetry for Calabi–Yau three-folds and K3 × T2

Betzler

Plauschinn

2018

Nuclear Physics B

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We perform dimensional reductions of type IIA and type IIB double field theory in the flux formulation on Calabi-Yau three-folds and on K3 × T 2 . In addition to geometric and non-geometric three-index fluxes and Ramond-Ramond fluxes, we include generalized dilaton fluxes. We relate our results to the scalar potentials of corresponding four-dimensional gauged supergravity theories, and we verify the expected behavior under mirror symmetry. For Calabi-Yau three-folds we extend this analysis to the full bosonic action including kinetic terms. Basics of Double Field TheoryThis section will provide a brief overview on the notions of DFT, which form the basis of our upcoming considerations. For more details, we would like to refer the reader to [26-28]. Doubled SpacetimeThe basic idea of DFT is to enhance ordinary supergravity theories with additional structures in a way that T-duality becomes a manifest symmetry. Motivated by the insights from toroidal compactifications of the bosonic string, one doubles the dimension of the D-dimensional spacetime manifold M by introducing additional winding coordinatesxm conjugate to the winding numberpm (just as the normal spacetime coordinates xm relate to the momenta pm) and arrange them in doubled coordinates XM = xm, xm , PM = pm, pm withm = 1, . . . D andM = 0, . . . 2D. (2.1)

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Complex/Symplectic Mirrors

Cited by 15 publications

References 36 publications

RR photons

RR photons

Geometric transitions on non‐Kähler manifolds

Dimensional reductions of DFT and mirror symmetry for Calabi–Yau three-folds and K3 × T2

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Complex/Symplectic Mirrors

Cited by 15 publications

References 36 publications

RR photons

RR photons

Geometric transitions on non‐Kähler manifolds

Dimensional reductions of DFT and mirror symmetry for Calabi–Yau three-folds and K3 × T2

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Dimensional reductions of DFT and mirror symmetry for Calabi–Yau three-folds and K3 × T2