Branes: from free fields to general backgrounds

Abstract

Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. A boundary condition is specified by two types of data: first, a consistent collection of reflection coefficients for bulk fields on the disk; and second, a choice of an automorphism $\omega$ of the fusion rules that preserves conformal weights. Non-trivial automorphisms $\omega$ correspond to D-brane configurations for arbitrary conformal field theories. The choice of the fusion rule automorphism $\omega$ amounts to fixing the dimension and certain global topological features of the D-brane world volume and the background gauge field on it. We present evidence that for fixed choice of $\omega$ the boundary conditions are classified as the irreducible representations of some commutative associative algebra, a generalization of the fusion rule algebra. Each of these irreducible representations corresponds to a choice of the moduli for the world volume of the D-brane and the moduli of the flat connection on it.

56 pages, LaTeX2e. Typos corrected; two references added

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Cited by in corpus (59)

• Boundary Conditions in Rational Conformal Field Theories
• Boundary Deformation Theory and Moduli Spaces of D-Branes
• On the structure of open-closed topological field theory in two dimensions
• Symmetry breaking boundaries I. General theory
• D-branes in group manifolds
• The geometry of WZW branes
• Orientifolds of Gepner Models
• Symmetry breaking boundaries II. More structures; examples
• Life at the Interface of Particle Physics and String Theory
• The many faces of Ocneanu cells
• Defect Lines and Boundary Flows
• Conformal boundary conditions and three-dimensional topological field theory
• Worldsheet approaches to D-branes on supersymmetric cycles
• Conformal Correlation Functions, Frobenius Algebras and Triangulations
• Landau-Ginzburg Realization of Open String TFT
• Lectures on Non-BPS Dirichlet branes
• Projections in string theory and boundary states for Gepner models
• Rational Conformal Field Theories and Complex Multiplication
• Lectures on Branes in Curved Backgrounds
• Comments on nonunitary conformal field theories
• D-Branes on K3-Fibrations
• D-branes in Gepner models and supersymmetry
• On the Landau-Ginzburg description of Boundary CFTs and special Lagrangian submanifolds
• Big Bang Models in String Theory
• On the hierarchy of symmetry breaking D-branes in group manifolds
• D-branes in an AdS_3 background
• D-branes in String theory Melvin backgrounds
• D-branes in curved spacetime: Nappi-Witten background
• Type I Vacua from Diagonal $Z_3$-Orbifolds
• Boundary Conformal Field Theory and Fusion Ring Representations
• Completeness of boundary conditions for the critical three-state Potts model
• Fundamental strings in Dp-Dq brane systems
• The action of outer automorphisms on bundles of chiral blocks
• Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on K3
• Strings, Branes and Extra Dimensions
• Notes on Orientifolds of Rational Conformal Field Theories
• Boundary States of c=1 and 3/2 Rational Conformal Field Theories
• On D-branes from Gauged Linear Sigma Models
• Orbifold analysis of broken bulk symmetries
• Crosscaps, Boundaries and T-Duality
• Geometry of WZW Orientifolds
• On Orientifolds of WZW Models and their Relation to Geometry
• D-Branes on ALE Spaces and the ADE Classification of Conformal Field Theories
• D-branes in Singular Calabi-Yau n-fold and N=2 Liouville Theory
• D0-branes in Gepner models and N=2 black holes
• Fermionization of conformal boundary states
• Dirichlet Branes on Orientifolds
• The classifying algebra for defects
• Boundary Rings and N=2 Coset Models
• RCFT with defects: Factorization and fundamental world sheets
• Integers in the open string
• Frobenius-Schur Indicators, the Klein-bottle Amplitude, and the Principle of Orbifold Covariance
• Free Field Construction of D-branes in N=2 Superconformal Minimal Models
• On Discrete Symmetries in su(2) and su(3) Affine Theories and Related Graphs
• The three-dimensional origin of the classifying algebra
• Coulomb-gas formulation of SU(2) branes and chiral blocks
• Inner brane: A D3-brane in the Nappi-Witten model from an inner group automorphism
• On Orientifolds of c=1 Orbifolds
• Bundles of chiral blocks and boundary conditions in CFT