The S-matrix of the AdS5xS5 superstring

According to the gauge-string duality conjecture, the spectrum of scaling dimensions of composite gauge invariant operators of the planar maximally supersymmetric Yang-Mills theory in four dimensions should be equivalent to the energy spectrum of superstrings propagating in the AdS5 x S5 space-time, where AdS5 is the five-dimensional Anti-de Sitter space and S5 is the five-dimensional sphere. We study strings on AdS5 x S5. The corresponding world-sheet theory exhibits the remarkable property of being integrable, that is it has an infinite number of conservation laws. The asymptotic spectrum of the world-sheet theory contains both the fundamental particles and bound states of the latter. We explicitly derive the S-matrix that describes scattering of arbitrary bound states. The key feature that enables this derivation is the so-called Yangian symmetry. Subsequently, we study the universal algebraic properties of the found S-matrix. As in many integrable models, the S-matrix plays a key role in the determination of the energy spectrum. In this context, we employ the Bethe ansatz approach to compute the large volume energy spectrum of string bound states.