Correspondence between noncommutative soliton and open string/D-brane system via Gaussian damping factor

The gaussian damping factor (g.d.f.) and the new interaction vertex with th e symplectic tenser are the characteristic properties of the N-point scalar -vector scattering amplitudes of the p - p ' (p < p ') open string system w hich realizes noncommutative geometry. The g.d.f. is here interpreted as a form factor of the Dp-brane by noncommutative U(1) current. Observing that the g.d.f. is in fact equal to the Fourier transform of the noncommutative projector soliton introduced by Gopakumar, Minwalla and Strominger, we furt her identify the Dp-brane in the zero slope limit with the noncommutative s oliton state. It is shown that the g.d.f. depends only on the total momentu m of N - 2 incoming/outgoing photons in the zero slope limit. In the descri ption of the low-energy effective action (LEEA) proposed before, this is sh own to follow from the delta function propagator and the form of the initia l/final wave functions in the soliton sector which resides in the x(m) (m = p + 1 . . . p ') dependent part of the scalar field Phi (x(u), x(m)). The three and four point amplitudes computed from LEEA agree with string calcul ation. We discuss related issues which are resummation/lifting of infinite degeneracy and conservation of momentum transverse to the Dp-brane.