  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.
