Complex/Symplectic Mirrors

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

doi:10.2172/878028

Cited by 20 publications

(36 citation statements)

References 27 publications

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“…A more ambitious program would have been to justify the forms to expand in ab initio. Though concrete proposals in this direction are lacking, one natural thought is that massive eigenforms of the Laplacian should play a role in the expansion [17,28]. In the following subsection, we study the relation between our ansatz in section 2 and an expansion in eigenforms of the Laplacian.…”

Section: Expanding In Eigenforms Of the Laplacianmentioning

confidence: 99%

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Towards reduction of type II theories on SU(3) structure manifolds

Kashani-Poor

Minasian

2007

J. High Energy Phys.

162

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Abstract:We revisit the reduction of type II supergravity on SU(3) structure manifolds conjectured to lead to gauged N = 2 supergravity in 4 dimensions. The reduction proceeds by expanding the invariant 2-and 3-forms of the SU(3) structure as well as the gauge potentials of the type II theory in the same set of forms, the analogues of harmonic forms in the case of Calabi-Yau reductions. By focussing on the metric sector, we arrive at a list of constraints these expansion forms should satisfy to yield a base point independent reduction. Identifying these constraints is a first step towards a first-principles reduction of type II on SU(3) structure manifolds.

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Section: Expanding In Eigenforms Of the Laplacianmentioning

confidence: 99%

“…We begin with a set of linearly independent 2-forms that are massive eigenforms of the Laplacian (rather than linear combinations of such) and coclosed ( [28] considers the following setup up to the proper normalization),…”

Section: A First Attempt At Constructing a Set Of Expansion Formsmentioning

confidence: 99%

Towards reduction of type II theories on SU(3) structure manifolds

Kashani-Poor

Minasian

2007

J. High Energy Phys.

162

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“…As Gualtieri showed [36] the generalized Kahler geometry (I, J ) is equivalent to the data (g, b, I + , I − ) with certain compatibility conditions, where g is an ordinary metric, B is a two-form and I + and I − are the ordinary complex structures. This geometry was encountered in a study of N = (2, 2) CFT in [85], and recently studied in works [86][87][88][89][90][91][92][93][94][95][96][97][98][99].…”

Section: The Bv Gauge Fixingmentioning

confidence: 99%

Topological strings in generalized complex space

Pestun¹

2007

Advances in Theoretical and Mathematical Physics

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A two-dimensional topological sigma-model on a generalized CalabiYau target space X is defined. The model is constructed in a BatalinVilkovisky formalism using only a generalized complex structure J and a pure spinor ρ on X. In the present construction, the algebra of Q-transformations automatically closes off-shell, the model transparently depends only on J , the algebra of observables and correlation functions for topologically trivial maps in genus zero are easily defined. The extended moduli space appears naturally. The familiar action of the twisted N = 2 conformal field theory (CFT) can be recovered after a gauge fixing. In the open case, we consider an example of generalized deformation of complex structure by a holomorphic Poisson bivector β and recover holomorphic noncommutative Kontsevich * -product.e-print archive: http://lanl.arXiv.org/abs/hep-th/0603145 1 On leave from ITEP, Moscow, 117259, Russia. VASILY PESTUN

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“…There are by now various sources of evidence suggesting that we should not restrict ourselves to the study of Calabi-Yau spaces as string theory vacua. The study of mirror symmetry for Calabi-Yau flux compactification, for instance, will inevitably lead us to the territory of "Non-Kählerity" [2,3,4,5,6,7] It is also very interesting to study the fate of the well-known IIA/hetrotic string duality if we compactify IIA string on the non-Kähler background. This nonpertubative duality between IIA on K3 fibered Calabi-Yau and heterotic string on K3×T 2 was first studied in [8,9] and then generalized to the case with fluxes and SU (3)-structure manifolds [13,11].…”

Section: Introductionmentioning

confidence: 99%