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The geometry of D-branes can be probed by open string scattering. If thebackground carries a non-vanishing B-field, the world-volume becomesnon-commutative. Here we explore the quantization of world-volume geometries ina curved background with non-zero Neveu-Schwarz 3-form field strength H = dB.Using exact and generally applicable methods from boundary conformal fieldtheory, we study the example of open strings in the SU(2) Wess-Zumino-Wittenmodel, and establish a relation with fuzzy spheres or certain (non-associative)deformations thereof. These findings could be of direct relevance for D-branesin the presence of Neveu-Schwarz 5-branes; more importantly, they provideinsight into a completely new class of world-volume geometries.Comment: 19 pages, LaTeX, 1 figure; some explanations improved, references  adde

Non-commutative worldvolume geometries: D-branes on SU(2) and fuzzy spheres