Worldsheet and Spacetime Properties of p-p' System with B Field and Noncommutative Geometry

Abstract

We study worldsheet and spacetime properties of the p-p&#39; (p < p&#39;) open string system with constant B_{ij} field viewed from the Dp&#39; brane. The description of this system in terms of the CFT with spin and twist fields leads us to consider the renormal ordering procedure from the SL(2,R) invariant vacuum to the oscillator vacuum. We compute the attendant two distinct superspace two-point functions as well as their difference (the subtracted two-point function). These bring us an integral (Koba-Nielsen) representation for the multiparticle tree scattering amplitudes consisting of N-2 vectors and two tachyons. We evaluate them explicitly for the N=3,4 cases. Several novel features are observed which include a momentum dependent multiplicative factor to each external vector leg and the emergence of a symplectic tensor multiplying the polarization vectors. In the zero slope limit, the principal parts of the amplitudes translate into a noncommutative field theory in p&#39;+1 dimensions in which a scalar field decaying exponentially in (p&#39;-p) dimensions and a noncommutative U(1) gauge field interact via the minimal coupling and a new interaction. A large number of nearly massless states noted before are shown to propagate in the t-channel.