Consistent Quantization of Noncommutative D-brane in Non-constant B Field Background

We perform the consistent quantization of open string D-brane in non-constant NS-NS closed string B field background by directly imposing the worldsheet conformal symmetry. In addition to the previous noncommutative D-brane coordinates quantization with constant noncommutative parameter $\theta$, we obtain a set of constraints on the B field which can be interpreted as a quantum consistent deformation of a curved noncommutative D-brane.