Star products from commutative string theory

A boundary-state computation is performed to obtain derivative corrections to the Chern-Simons coupling between a p-brane and the RR gauge potential C ^p −3. We work to quadratic order in the gauge field strength F, but all orders in derivatives. In a certain limit, which requires the presence of a constant B-field background, it is found that these corrections neatly sum up into the *₂ product of (commutative) gauge fields. The result is in agreement with a recent prediction using noncommutativity.