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2010

Topological boundary conditions in abelian Chern-Simons theory

Kapustin, Anton, Saulina, Natalia

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We study topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries.

From a 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.

Topological boundary conditions in abelian Chern-Simons theory · Around

Built on

A. Joyal, R. Street, “Braided tensor categories”, Adv. Math. 102, 20-78, 1983
1983
Earlier work this paper cites.
B. Bakalov and A. A. Kirillov, “Lectures on tensor categories and modular functors,” American Mathematical Society, 2000
2000
Earlier work this paper cites.

Similar

A. Kapustin and M. Tikhonov, “Abelian duality, walls and boundary conditions in diverse dimensions,” JHEP 0911
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2009
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A. Kapustin, “Topological Field Theory, Higher Categories, and Their Applications,” arXiv:1004.2307 [math.QA]
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D. Belov, G. Moore,“Classification of abelian spin Chern-Simons theories”, hep-th/0505235
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D. Gaiotto and E. Witten, “S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory,” arXiv:0807.3720 [hep-th]
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S. D. Stirling, “Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories,” arXiv:0807.2857 [hep-th]
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E. Witten, “Quantum field theory and the Jones polynomial”, Com. Math. Phys. 121, 351-399
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E. Witten, “SL(2,Z) action on three-dimensional conformal field theories with Abelian symmetry,” arXiv:hep-th/0307041
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V. V. Nikulin, “Integral symmetric bilinear forms and their applications”, Math. USSR. Izvestija Vol. 14, p. 103
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A. Kapustin and L. Rozansky,“Three-dimensional topological field theory and symplectic algebraic geometry II,” arXiv:0909.3643 [math.AG]
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D. S. Freed, M. J. Hopkins, J. Lurie and C. Teleman, “Topological Quantum Field Theories from Compact Lie Groups,” arXiv:0905.0731 [math.AT]
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Cited in the paper.

Then

A. Kapustin, L. Rozansky and N. Saulina, “Three-dimensional topological field theory and symplectic algebraic geometry I,” Nucl. Phys. B 816
Original
2009
Later among the works it cites.

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