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Three-dimensional topological field theory and symplectic algebraic geometry I

Kapustin, Anton and Rozansky, Lev and Saulina, Natalia (2009) Three-dimensional topological field theory and symplectic algebraic geometry I. Nuclear Physics B, 816 (3). pp. 295-355. ISSN 0550-3213.

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We study boundary conditions and defects in a three-dimensional topological sigma-model with a complex symplectic target space X (the Rozansky–Witten model). We show that boundary conditions correspond to complex Lagrangian submanifolds in X equipped with complex fibrations. The set of boundary conditions has the structure of a 2-category; morphisms in this 2-category are interpreted physically as one-dimensional defect lines separating parts of the boundary with different boundary conditions. This 2-category is a categorification of the Z_2-graded derived category of X; it is also related to categories of matrix factorizations and a categorification of deformation quantization (quantization of symmetric monoidal categories). In Appendix B we describe a deformation of the B-model and the associated category of branes by forms of arbitrary even degree.

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Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2009 Elsevier B.V. Received 26 November 2008; accepted 28 January 2009. Available online 3 February 2009. A.K. would like to thank Alexei Bondal, Dennis Gaitsgory, David Ben-Zvi, David Nadler, Dan Freed, Andrei Mikhailov, and Dima Orlov for discussions. L.R. would like to thank Dima Arinkin, David Ben-Zvi and David Nadler for discussions. N.S. would like to thank Andrei Mikhailov for discussions. Part of this work was done during the BIRS workshop “Matrix Factorizations in Physics and Mathematics”, May 2008. A.K. and L.R. are grateful to the organizers for the invitation and to the Banff International Research Station for hospitality. The work of A.K. and N.S. was supported in part by the DOE grant DE-FG03-92-ER40701. The work of L.R. was supported by NSF grant DMS-0808974.
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Department of Energy (DOE)DE-FG03-92-ER40701
Issue or Number:3
Record Number:CaltechAUTHORS:20090818-093340561
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15151
Deposited By: Tony Diaz
Deposited On:19 Aug 2009 03:20
Last Modified:03 Oct 2019 00:55

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