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Topological boundary conditions in abelian Chern-Simons theory

Kapustin, Anton and Saulina, Natalia (2011) Topological boundary conditions in abelian Chern-Simons theory. Nuclear Physics B, 845 (3). pp. 393-435. ISSN 0550-3213. http://resolver.caltech.edu/CaltechAUTHORS:20110310-100106179

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Abstract

We study topological boundary conditions in abelian Chern–Simons theory and line operators confined to such boundaries. From the mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern–Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern–Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.nuclphysb.2010.12.017 DOIArticle
http://www.sciencedirect.com/science/article/pii/S0550321310006723PublisherArticle
http://arxiv.org/abs/1008.0654arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2010 Elsevier B.V. Received 24 September 2010; accepted 27 December 2010. Available online 30 December 2010. We would like to thank D. Freed, A. Kitaev, J. Lurie, G. Moore, V. Ostrik, and L. Rozansky for useful discussions and advice. We are grateful to the Aspen Center for Physics for an excellent working atmosphere. This work was supported in part by the DOE grant DE-FG02-92ER40701.
Group:Caltech Theory
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-92ER40701
Record Number:CaltechAUTHORS:20110310-100106179
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110310-100106179
Official Citation:Anton Kapustin, Natalia Saulina, Topological boundary conditions in abelian Chern-Simons theory, Nuclear Physics B, Volume 845, Issue 3, 21 April 2011, Pages 393-435, ISSN 0550-3213, DOI: 10.1016/j.nuclphysb.2010.12.017.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22798
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:10 Mar 2011 18:40
Last Modified:27 Oct 2017 18:33

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