Noncommutativity in string theory and D-branes

String theory in a constant B-field exhibits noncommutative structure of space–time. By considering the B-field dynamical and studying its interaction with Ramond–Ramond (RR) background we observe the breaking of the B-field gauge symmetry in the effective action. This effect takes place due to nonperturbative coupling of the B-field to membrane topological charge. As a result, the B-field is renormalized in the RR backgrounds, making it impossible to obtain consistent noncommutative models with constant B-field. We argue that the gauge invariance should be restored by introducing appropriate external D-brane configuration.