Journal
NUCLEAR PHYSICS B
Volume 845, Issue 3, Pages 393-435Publisher
ELSEVIER
DOI: 10.1016/j.nuclphysb.2010.12.017
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Funding
- DOE [DE-FG02-92ER40701]
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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. (C) 2010 Published by Elsevier B.V.
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