The S-matrix of string bound states

We find the S-matrix which describes the scattering of two-particle bound states of the light-cone string sigma model on AdS5×S5. We realize the M-particle bound state representation of the centrally extended su(2|2) algebra on the space of homogeneous (super)symmetric polynomials of degree M depending on two bosonic and two fermionic variables. The scattering matrix SMN of M- and N-particle bound states is a differential operator of degree M+N 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 M=1,N=2 and M=N=2. 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 x1+,x1−,x2+,x2− is universal for scattering of any bound states, it obeys a crossing symmetry equation which depends on M and N.