A classifying algebra for boundary conditions
arXiv:hep-th/9708141 · doi:10.1016/S0370-2693(97)01180-5
Abstract
We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer spin simple current, modular invariant), this classifying algebra contains the fusion algebra of the untwisted sector as a subalgebra. Proper treatment of fields in the twisted sector, so-called fixed points, leads to structures that are intriguingly close to the ones implied by modular invariance for conformal field theories on closed orientable surfaces.
12 pages, LaTeX
Cited by in corpus (46)
- Boundary Conditions in Rational Conformal Field Theories
- D-branes in Gepner models
- Boundary Deformation Theory and Moduli Spaces of D-Branes
- TFT construction of RCFT correlators III: Simple currents
- Supersymmetry breaking, open strings and M-theory
- Boundary structure constants for the A-series Virasoro minimal models
- Symmetry breaking boundaries I. General theory
- The geometry of WZW branes
- Permutation Branes
- Boundaries, crosscaps and simple currents
- Symmetry breaking boundaries II. More structures; examples
- The conformal boundary states for SU(2) at level 1
- Branes: from free fields to general backgrounds
- Charged and Uncharged D-branes in various String Theories
- Conformal Correlation Functions, Frobenius Algebras and Triangulations
- Projections in string theory and boundary states for Gepner models
- Lectures on Branes in Curved Backgrounds
- Quantum brownian motion on a triangular lattice and c=2 boundary conformal field theory
- Spectra of 4D, N=1 Type I String Vacua on Non-Toroidal CY Threefolds
- Fixed point resolution in extended WZW-models
- Structure constants for the D-series Virasoro minimal models
- Type IIB orientifolds on Gepner points
- Fermionic CFTs and classifying algebras
- Completeness of boundary conditions for the critical three-state Potts model
- Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on K3
- Boundary States of c=1 and 3/2 Rational Conformal Field Theories
- Crosscaps, Boundaries and T-Duality
- Generalised N=2 permutation branes
- Fermionization and boundary states in 1+1 dimensions
- D-branes in Singular Calabi-Yau n-fold and N=2 Liouville Theory
- Boundaries, defects and Frobenius algebras
- Fermionization of conformal boundary states
- Open Descendants of Non-Diagonal Invariants
- Twisted CFT and bilayer Quantum Hall systems
- The classifying algebra for defects
- Twisted boundary states and representation of generalized fusion algebra
- Orientation matters for NIMreps
- Super D-branes from BRST Symmetry
- Heterotic-Type II duality and wrapping rules
- Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
- On Discrete Symmetries in su(2) and su(3) Affine Theories and Related Graphs
- Twisted boundary states in c=1 coset conformal field theories
- Landau-Ginzburg Description of Boundary Critical Phenomena in Two Dimensions
- The three-dimensional origin of the classifying algebra
- Coulomb-gas formulation of SU(2) branes and chiral blocks
- On Orientifolds of c=1 Orbifolds