Open strings in Lie groups and associative products
arXiv:hep-th/0610329 · doi:10.1016/j.nuclphysb.2007.05.029
Abstract
Firstly, we generalize a semi-classical limit of open strings on D-branes in group manifolds. The limit gives rise to rigid open strings, whose dynamics can efficiently be described in terms of a matrix algebra. Alternatively, the dynamics is coded in group theory coefficients whose properties are translated in a diagrammatical language. In the case of compact groups, it is a simplified version of rational boundary conformal field theories, while for non-compact groups, the construction gives rise to new associative products. Secondly, we argue that the intuitive formalism that we provide for the semi-classical limit, extends to the case of quantum groups. The associative product we construct in this way is directly related to the boundary vertex operator algebra of open strings on symmetry preserving branes in WZW models, and generalizations thereof, e.g. to non-compact groups. We treat the groups SU(2) and SL(2,R) explicitly. We also discuss the precise relation of the semi-classical open string dynamics to Berezin quantization and to star product theory.
47 pages, 14 figures
References in corpus (33)
- String Theory and Noncommutative Geometry
- Noncommutative Field Theory
- D-branes and Deformation Quantization
- Invasion of the Giant Gravitons from Anti-de Sitter Space
- Toeplitz Quantization of Kähler Manifolds and
- Magnetic fields, branes and noncommutative geometry
- D-branes in the WZW model
- Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
- Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))
- Strings in AdS_3 and the SL(2,R) WZW Model. Part 3: Correlation Functions
- Completeness Conditions for Boundary Operators in 2D Conformal Field Theory
- Boundary Conditions in Rational Conformal Field Theories
- Symplectic structures associated to Lie-Poisson groups
- Boundary Liouville Field Theory: Boundary Three Point Function
- H(3)+ correlators from Liouville theory
- Boundary structure constants for the A-series Virasoro minimal models
- The geometry of WZW branes
- Gauged WZW models and Non-abelian duality
- Nonsemisimple Sugawara Constructions
- Knizhnik-Zamolodchikov equations and spectral flow in AdS3 string theory
- String interactions in gravitational wave backgrounds
- Non-commutative gauge theory of twisted D-branes
- D-branes and BCFT in Hpp-wave backgrounds
- The Fuzzy Sphere Star-Product and Spin Networks
- Semiclassical Limits of Extended Racah Coefficients
- Coherent States for Quantum Compact Groups
- Strict quantization of coadjoint orbits
- Quadratic brackets from symplectic forms
- Quantisation of a particle moving on a group manifold
- Gauge Theories and Fibre Bundles - Applications to Particle Dynamics
- Three-dimensional black hole entropy
- Path Integral Quantization of the Symplectic Leaves of the SU(2)* Poisson-Lie Group
- Strings, Dipoles and Fuzzy Spheres