The S-matrix of String Bound States

TL;DR

This paper derives the S-matrix for scattering of two-particle bound states in the light-cone string sigma model on AdS5xS5, ensuring it satisfies key symmetries and equations, and explores its properties for various bound state configurations.

Contribution

It explicitly constructs the bound state S-matrix as a differential operator acting on symmetric polynomials, extending the understanding of scattering in AdS/CFT correspondence.

Findings

Derived the S-matrix for M- and N-particle bound states.

Confirmed the S-matrix satisfies Yang-Baxter, unitarity, CPT, parity, and crossing symmetry.

Analyzed the crossing symmetry of the dressing factor for different bound states.

Abstract

We find the S-matrix which describes the scattering of two-particle bound states of the light-cone string sigma model on AdS5xS5. 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 S^{MN} 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 x_1^+,x_1^-,x_2^+,x_2^- is universal for scattering of any bound states, it obeys a crossing symmetry equation which depends on M and N.