Factorized world-sheet scattering in near-flat

Abstract

We show the factorization of the three-particle world-sheet S-matrix of AdS 5 ×S 5 superstring theory in the near-flat-space limit at one loop order. This is done by computing various scattering amplitudes from Feynman diagrams in the world-sheet theory. The knowledge of certain highest weight amplitudes allows us to fix all the freedom in the three-particle Smatrix, which we argue to be constrained up to four scalar functions due to the symmetries of the model. We demonstrate that these amplitudes are given by corresponding products of the known two-particle S-matrix elements, from which it follows that the scattering of any three worldsheet excitations factorizes. This provides an explicit and direct check of the quantum integrability of string theory in near-flat AdS 5 × S 5 as it renders evidence for the existence of higher conserved charges. By computing further amplitudes we also obtain an indirect confirmation of the supersymmetries of the near-flat-space model.

Classifying integrable symmetric space strings via factorized scattering

“…Beyond the construction of the Lax connection much evidence has been accumulated for the integrability of the string also at the quantum level. Most relevant to our discussion here is the formulation of an exact worldsheet S-matrix [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] which matches with perturbative worldsheet calculations up to two loops in some cases [18,[41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

Remarks on the geometrical properties of semiclassically quantized strings

“…We discuss the gauge-fixing and 3 In another kind of perturbative analysis of the worldsheet σ-model, i.e. the perturbative evaluation of the massive S-matrix for the elementary excitations around the BMN vacuum [44][45][46] (see also [15,47] for reviews), the one-loop computation for the full AdS5 × S 5 case [48][49][50] (in a certain regularization scheme) reproduces exactly the results [51] predicted by (symmetries and) quantum integrability. the decoupling of the longitudinal modes, as well as the arising of gauge connections in the covariant derivatives associated to the structure of normal bundle.…”

Two-dimensional S-matrices from unitarity cuts

“…The scattering of the world-sheet excitations has been studied at tree-level in [7], while one-loop [8] and twoloop [9] results have been carried out only in the simpler near-flat-space limit [70] where interactions are at most quartic in the fields. These studies have also explicitly shown some consequences of the integrability of the model, such as the factorization of the many-body S-matrix and the absence of particle production in the scattering processes [71].…”