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Topological strings on noncommutative manifolds

Kapustin, Anton (2004) Topological strings on noncommutative manifolds. International Journal of Geometric Methods in Modern Physics, 1 (2). pp. 49-81. ISSN 0219-8878. https://resolver.caltech.edu/CaltechAUTHORS:20160505-104335472

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Abstract

We identify a deformation of the N=2 supersymmetric sigma model on a Calabi–Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkähler X such deformations allow one to interpolate continuously between the A-model and the B-model. For generic values of the noncommutativity and the B-field, properties of the topologically twisted sigma-models can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigma-model is localized on generalized holomorphic maps, whereas for the A-model and the B-model it is localized on holomorphic and constant maps, respectively. The geometry of topological D-branes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological D-branes, which includes A-branes and B-branes as special cases.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1142/S0219887804000034DOIArticle
http://www.worldscientific.com/doi/abs/10.1142/S0219887804000034PublisherArticle
https://arxiv.org/abs/hep-th/0310057arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2004 World Scientific Publishing. Received: 29 October 2003; Revised: 24 November 2003. I would like to thank Marco Gualtieri, Nigel Hitchin, and Dmitri Orlov for discussions. I also would like to thank the organizers of the workshop “Geometry and Topology of Strings” at KITP, UC Santa Barbara, July-August 2004, for a very stimulating meeting. This research was supported in part by the DOE grant DE-FG03-92-ER40701.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
Subject Keywords:Topological sigma-models; topological D-branes; noncommutative geometry
Issue or Number:2
Record Number:CaltechAUTHORS:20160505-104335472
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160505-104335472
Official Citation:TOPOLOGICAL STRINGS ON NONCOMMUTATIVE MANIFOLDS ANTON KAPUSTIN International Journal of Geometric Methods in Modern Physics 2004 01:01n02, 49-81
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66684
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 May 2016 22:13
Last Modified:03 Oct 2019 09:58

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