Factorization and generalized *-products

Abstract

The generalized * products, or the *(N) products, appear both in the one-loop effective action of noncommutative Yang-Mills theories and in the coupling of a closed string to N open strings on a disk when the D-brane world-volume is noncommutative. Factorization of the string amplitudes provides a uniform understanding of the sn-products and a hint to obtain a simple, explicit formula (in the momentum space) for arbitrary N in the non-Abelian case. Possible extension to a more general (M)*(N)-product in the M-loop context is discussed.