2006/10/31 by Pierre Bieliavsky, Charles Jego, Jan Troost
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Associative property #Black Holes and Theoretical Physics #Classical limit #Group (periodic table) #Lie algebra #Lie group #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Operator algebra #Physics #Pure mathematics #Quantum #Quantum mechanics #Star product #String theory #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2007.05.029
published as Nucl.Phys.B782:94-133,2007 · 47 pages, 14 figures
arxiv created 2006/10/31 · openalex publication_date 2007/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.