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Remarks on A-branes, mirror symmetry, and the Fukaya category

Kapustin, Anton and Orlov, Dmitri (2003) Remarks on A-branes, mirror symmetry, and the Fukaya category. Journal of Geometry and Physics, 48 (1). pp. 84-99. ISSN 0393-0440. https://resolver.caltech.edu/CaltechAUTHORS:20160506-093522683

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Abstract

We discuss D-branes of the topological A-model (A-branes), which are believed to be closely related to the Fukaya category. We give string theory arguments which show that A-branes are not necessarily Lagrangian submanifolds in the Calabi–Yau: more general coisotropic branes are also allowed, if the line bundle on the brane is not flat. We show that a coisotropic A-brane has a natural structure of a foliated manifold with a transverse holomorphic structure. We argue that the Fukaya category must be enlarged with such objects for the Homological Mirror Symmetry Conjecture to be true.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/S0393-0440(03)00026-3DOIArticle
http://www.sciencedirect.com/science/article/pii/S0393044003000263PublisherArticle
https://arxiv.org/abs/hep-th/0109098arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Orlov, Dmitri0000-0002-2230-457X
Additional Information:© 2003 Elsevier Science B.V. Received 31 May 2002, Accepted 28 January 2003, Available online 2 April 2003. We are grateful to Dan Freed for useful suggestions and to Ezra Getzler for pointing out the relevance of bihamiltonian geometry. Some preliminary results have been presented by AK at the Duality Workshop, ITP, Santa Barbara, 18 June–13 July, 2001. AK would like to thank Ron Donagi, Dan Freed, Ezra Getzler, Tony Pantev, and other participants for stimulating discussions, and the organizers for making this workshop possible. AK was supported in part by DOE grants DE-FG02-90ER40542 and DE-FG03-92-ER40701. DO was supported in part by RFFI grant 99-01-01144 and a grant for support of leading scientific groups N 00-15-96085. The research described in this publication was made possible in part by Award No RMl-2089 of the US. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF).
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-90ER40542
Department of Energy (DOE)DE-FG03-92-ER40701
Russian Foundation for Fundamental Investigations (RFFI)99-01-01144
Russian Foundation for Fundamental Investigations (RFFI)N 00-15-96085
Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF)RM1-2089
Subject Keywords:A-branes; Mirror symmetry; The Fukaya category
Issue or Number:1
Classification Code:MSC: 81T30
Record Number:CaltechAUTHORS:20160506-093522683
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160506-093522683
Official Citation:Anton Kapustin, Dmitri Orlov, Remarks on A-branes, mirror symmetry, and the Fukaya category, Journal of Geometry and Physics, Volume 48, Issue 1, October 2003, Pages 84-99, ISSN 0393-0440, http://dx.doi.org/10.1016/S0393-0440(03)00026-3. (http://www.sciencedirect.com/science/article/pii/S0393044003000263)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66713
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:06 May 2016 19:02
Last Modified:03 Oct 2019 09:59

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