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Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds

Grange, Pascal and Schäfer-Nameki, Sakura (2007) Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds. Journal of High Energy Physics, 2007 (10). Art. No. 052. ISSN 1126-6708.

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Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror hat M, it is argued that the product M × hat M is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and hat M. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3) × SU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry.

Item Type:Article
Additional Information:© 2007 SISSA. Received 31 August 2007, accepted for publication 26 September 2007. Published 12 October 2007. We thank Mariana Graña, Jan Louis, Luca Martucci, Ron Reid-Edwards, Bastiaan Spanjaard and Jie Yang for discussions and useful correspondence. P.G. is funded by the German-Israeli Foundation for Scientific Research and Development. S.S.N. is funded by a Caltech John A. McCone Postdoctoral Fellowship in Theoretical Physics and thanks Jan Louis for hospitality at the II. Institut für theoretische Physik of the University of Hamburg. This work was supported in part by the DFG and the European RTN Program MRTN-CT-2004-503369. E-print number: 0708.2392
Subject Keywords:D-branes; Differential and Algebraic Geometry
Issue or Number:10
Record Number:CaltechAUTHORS:GRAjhep07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9021
Deposited By: Archive Administrator
Deposited On:20 Oct 2007
Last Modified:02 Oct 2019 23:56

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