Topological boundary conditions in abelian Chern-Simons theory

2010/08/31 by Anton Kapustin, Natalia Saulina · 5 citations
Physics and Astronomy · Mathematics · #hep-th #math.QA

paper · pdf · doi:10.1016/j.nuclphysb.2010.12.017

published as Nucl.Phys.B845:393-435,2011 · 43 pages, latex

arxiv created 2010/09/21 · arxiv updated 2011/03/07

Abstract

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. 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.

Cited by

• Vine Codes: Low-Overhead Quantum LDPC Codes on a Planar Square Grid
• 3D Gravity Does Not Average Like Narain at Genus One: Rigidity of Virasoro Topological Boundaries
• An Effective String Theory Toolbox for Quantum Hall Interfaces I: Worldsheet Kinematics and Constraint Structure
• Planar quantum low-density parity-check codes with open boundaries
• Holographic duality from Howe duality: Chern-Simons gravity as an ensemble of code CFTs

Related

• On topological defects in Chern-Simons theory
• Homotopical analysis of 4d Chern-Simons theory and integrable field theories
• Chern-Simons Gauge Invariance and Boundary Conformal Fields
• Bicategories for boundary conditions and for surface defects in 3-d TFT
• Fermionic CFTs from topological boundaries in abelian Chern-Simons theories