The S-matrix of string bound states Original Research Article

We find the S-matrix which describes the scattering of two-particle bound states of the light-cone string sigma model on image. We realize the M-particle bound state representation of the centrally extended image algebra on the space of homogeneous (super)symmetric polynomials of degree M depending on two bosonic and two fermionic variables. The scattering matrix image of M- and N-particle bound states is a differential operator of degree image acting on the product of the corresponding polynomials. We require this operator to obey the invariance condition and the Yang–Baxter equation, and we determine it for the two cases image and image. We show that the S-matrices found satisfy generalized physical unitarity, CPT invariance, parity transformation rule and crossing symmetry. Although the dressing factor as a function of four parameters image is universal for scattering of any bound states, it obeys a crossing symmetry equation which depends on M and N.