T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology
TLDR
In this article, it was shown that every principal T2-bundle with H-flux does indeed have a T-dual, but in the missing cases (which we characterize in this paper) it is a non-classical and is a bundle of non-commutative tori.Abstract:
It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do not necessarily have a T-dual which is a torus bundle. A big puzzle has been to explain these mysterious “missing T-duals.” Here we show that this problem is resolved using noncommutative topology. It turns out that every principal T2-bundle with H-flux does indeed have a T-dual, but in the missing cases (which we characterize), the T-dual is non-classical and is a bundle of noncommutative tori. The duality comes with an isomorphism of twisted K-theories, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced by an isomorphism of twisted cyclic homology.read more
Citations
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Nongeometric Flux Compactifications
TL;DR: In this paper, a simple class of type II string compactifications which incorporate nongeometric "fluxes" in addition to "geometric flux" and the usual H-field and R-R fluxes are investigated.
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D-instantons and twistors
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References
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Alain Connes,Michael R. Douglas,Michael R. Douglas,Albert Schwarz,Albert Schwarz,Albert Schwarz +5 more
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Mirror symmetry is T duality
TL;DR: In this paper, it was argued that every Calabi-Yau manifold X with a mirror Y admits a family of supersymmetric toroidal 3-cycles and that the moduli space of such cycles together with their flat connections is precisely the space Y.
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Simplicial objects in algebraic topology
TL;DR: Simplicial Objects in Algebraic Topology as discussed by the authors has been the standard reference for the theory of simplicial sets and their relationship to the homotopy theory of topological spaces.