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Topological sigma-models with H-flux and twisted generalized complex manifolds

Kapustin, Anton and Li, Yi (2007) Topological sigma-models with H-flux and twisted generalized complex manifolds. Advances in Theoretical and Mathematical Physics, 11 (2). pp. 269-290. ISSN 1095-0761.

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We study the topological sector of N = 2 sigma-models with HH-flux. It has been known for a long time that the target-space geometry of these theories is not Kähler and can be described in terms of a pair of complex structures, which do not commute, in general, and are parallel with respect to two different connections with torsion. Recently an alternative description of this geometry was found, which involves a pair of commuting twisted generalized complex structures on the target space. In this paper, we define and study the analogs of A and B-models for N = 2 sigma-models with HH-flux and show that the results are naturally expressed in the language of twisted generalized complex geometry. For example, the space of topological observables is given by the cohomology of a Lie algebroid associated to one of the two twisted generalized complex structures. We determine the topological scalar product, which endows the algebra of observables with the structure of a Frobenius algebra. We also discuss mirror symmetry for twisted generalized Calabi-Yau manifolds.

Item Type:Article
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URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2007 International Press. A.K. is grateful to Andrew Frey, Marco Gualtieri, and Misha Verbitsky for advice. Y.L. would like to thank Vadim Borokhov, Takuya Okuda, and Xinkai Wu for helpful discussions. This work was supported in part by the DOE grant DE-FG03-92-ER40701.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
Issue or Number:2
Record Number:CaltechAUTHORS:20160505-115113631
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66694
Deposited By: Tony Diaz
Deposited On:05 May 2016 21:30
Last Modified:03 Oct 2019 09:59

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