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D-branes in Landau-Ginzburg models and algebraic geometry

Kapustin, Anton and Li, Yi (2003) D-branes in Landau-Ginzburg models and algebraic geometry. Journal of High Energy Physics, 2003 (12). Art. No. 005. ISSN 1029-8479. http://resolver.caltech.edu/CaltechAUTHORS:KAPjhep03

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Abstract

We study topological D-branes of type B in N = 2 Landau-Ginzburg models, focusing on the case where all vacua have a mass gap. In general, tree-level topological string theory in the presence of topological D-branes is described mathematically in terms of a triangulated category. For example, it has been argued that B-branes for an N = 2 sigma-model with a Calabi-Yau target space are described by the derived category of coherent sheaves on this space. M. Kontsevich previously proposed a candidate category for B-branes in N = 2 Landau-Ginzburg models, and our computations confirm this proposal. We also give a heuristic physical derivation of the proposal. Assuming its validity, we can completely describe the category of B-branes in an arbitrary massive Landau-Ginzburg model in terms of modules over a Clifford algebra. Assuming in addition Homological Mirror Symmetry, our results enable one to compute the Fukaya category for a large class of Fano varieties. We also provide a (somewhat trivial) counter-example to the hypothesis that given a closed string background there is a unique set of D-branes consistent with it.


Item Type:Article
Additional Information:Copyright © Institute of Physics and IOP Publishing Limited 2003. Received 20 August 2003, accepted for publication 3 December 2003. Published 2 February 2004. We are deeply grateful to Maxim Kontsevich for sharing with us his ideas about B-branes in Landau-Ginzburg models, and to Alexander Polishchuk for pointing out the relevance of non-homogeneous Koszul duality. We also thank Kentaro Hori and Dmitri Orlov for reading a preliminary draft of the paper and making a number of valuable comments. The first author would like to thank Institut des Hautes Etudes Scientifiques for hospitality during the writing of this paper. This work was supported in part by the DOE grant DE-FG03-92-ER40701.
Subject Keywords:topological field theories; D-branes; differential and algebraic geometry
Record Number:CaltechAUTHORS:KAPjhep03
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KAPjhep03
Alternative URL:http://dx.doi.org/10.1088/1126-6708/2003/12/005
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3081
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 May 2006
Last Modified:26 Dec 2012 08:52

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