Topological boundary conditions in abelian Chern-Simons theory
By A. Kapustin, N. Saulina. 2010
214 citations recorded by the source corpus.
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. pi-strings-195
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/41e9c34a12bb254e9f8d0e0b6d4243644d360606
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- E. Witten
- Sergei Gukov
- N. Seiberg
- Abhijit Gadde
- Cyril Closset
- Pavel Putrov
- D. Gaiotto
- Z. Komargodski
In Mathematical Physics
- E. Witten
- Sergei Gukov
- Cyril Closset
- Abhijit Gadde
- Z. Komargodski
- A. Kapustin
- T. Dumitrescu
- Pavel Putrov
Citations in the corpus
- Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions (2017, background): “The gapped boundary/interface criteria studied by Haldane [77], Kapustin-Saulina [62], Kitaev-Kong [63], LanWang-Wen [64, 68] and many others can be viewed as gauge symmetry-breaking [64–66, 68] or the Anderson-Higgs effect.”
- Coupling a QFT to a TQFT and duality (2014, background): “This is a special case of the observation that topological boundary conditions in Abelian Chern-Simons theories correspond to maximal isotropic subgroups in the gauge group [32].”
- Symmetries and Strings in Field Theory and Gravity (2010, background): “In this case we find a U(1) × U(1) Lagrangian description of the three dimensional Zp, level k, Chern-Simons gauge theory of [58,59] (see also the recent discussions [60,61]) ip 2π B ∧ dA+ ik 4π A ∧ dA .”
- Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward (2022, background): “A Lagrangian subgroup A is a subset of Abelian bosons in the topological order that are closed under fusion, have trivial mutual statistics, and that every other anyon braids non-trivially with at least one of the anyons in the subgroup[77, 78].”
- Comments on Chern-Simons contact terms in three dimensions (2012, methodology): “In order to compute the contact term κ corresponding to jµ, we naively integrate out the dynamical field Aµ to obtain an effective Lagrangian for aµ, Leff = iκ 4π εµνρaµ∂νaρ , κ = q − p2 k .”
- Fivebranes and 4-manifolds (2013, background): “and a Q/Z-valued quadratic form q on D [45].”
- Anyon condensation and tensor categories (2013, background): “So in this case, we recover the result in [44,56,1].”