Boundaries, defects and Frobenius algebras

Abstract

The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new computational tools. The construction of CFT correlators based on combining tools from topological field theory and non-commutative algebra in tensor categories, which we summarize in this contribution, allows e.g. to discuss, apart from boundary conditions, also defect lines and disorder fields.

arXiv comment7 pages. Contribution to the 35th International Symposium Ahrenshoop on the Theory of Elementary Particles (Berlin, August 2002) and to the International Conference on Theoretical Physics (UNESCO, Paris, July 2002). For related proceedings contributions see http://tpe.physik.rwth-aachen.de/schweigert/proceedings.html

References in corpus (9)

• TFT construction of RCFT correlators I: Partition functions
• Completeness Conditions for Boundary Operators in 2D Conformal Field Theory
• Systematic approach to cyclic orbifolds
• Characters and modular properties of permutation orbifolds
• Permutation Branes
• Conformal boundary conditions and three-dimensional topological field theory
• Conformal Correlation Functions, Frobenius Algebras and Triangulations
• A classifying algebra for boundary conditions
• Modular categories and orbifold models

Cited by in corpus (14)

• Diagrammatics for Bose condensation in anyon theories
• Defect Lines and Boundary Flows
• Loop Operators and the Kondo Problem
• K-Theory from a physical perspective
• Defects and Permutation branes in the Liouville field theory
• Symmetry breaking, permutation D-branes on group manifolds: boundary states and geometric description
• Phase boundaries in algebraic conformal QFT
• Generalised Permutation Branes on a product of cosets $G_{k_1}/H\times G_{k_2}/H$
• Entanglement Entropy of Topological Orders with Boundaries
• Canonical quantization of the WZW model with defects and Chern-Simons theory
• On the classification of duality defects in $c=2$ compact boson CFTs with a discrete group orbifold
• A duality Hopf algebra for holomorphic N=1 special geometries
• The universality question for noncommutative quantum field theory
• Quasi-Hamiltonian bookkeeping of WZNW defects