Non-commutative world-volumes: branes on SU(2) and fuzzy spheres

Alekseev, Anton Yu.; Recknagel, Andreas; Schomerus, Volker

doi:10.1088/1126-6708/1999/09/023

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Non-commutative world-volumes: branes on SU(2) and fuzzy spheres

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Recknagel, Andreas
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Alekseev, A. Y., Recknagel, A., & Schomerus, V. (1999). Non-commutative world-volumes: branes on SU(2) and fuzzy spheres. Journal of High Energy Physics, 1999(9): 023. doi:10.1088/1126-6708/1999/09/023.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5867-6

Abstract

The geometry of D-branes can be probed by open string scattering. If the background carries a non-vanishing B-field, the world-volume becomes non-commutative. Here we explore the quantization of world-volume geometries in a curved background with non-zero Neveu-Schwarz 3-form field strength H = dB. Using exact and generally applicable methods from boundary conformal field theory, we study the example of open strings in the SU(2) Wess-Zumino-Witten model, and establish a relation with fuzzy spheres or certain (non-associative) deformations thereof. These findings could be of direct relevance for D-branes in the presence of Neveu-Schwarz 5-branes; more importantly, they provide insight into a completely new class of world-volume geometries.