Two - loop test of the N = 6 Chern - Simons theory S - matrix

Starting from the integrable two-loop spin-chain Hamiltonian describing the anomalous dimensions of scalar operators in the planar N = 6 superconformal Chern-Simons theory of ABJM, we perform a direct coordinate Bethe ansatz computation of the corresponding two-loop S-matrix. The result matches with the weak-coupling limit of the scalar sector of the all-loop S-matrix which we have recently proposed. In particular, we confirm that the scattering of A and B particles is reflectionless. As a warm up, we first review the analogous computation of the one-loop S-matrix from the one-loop dilatation operator for the scalar sector of planar N = 4 superconformal Yang-Mills theory, and compare the result with the all-loop SU(2|2)2 S-matrix. 1 Department of Physics, Ewha Womans University, Seoul 120-750, South Korea 2 Physics Department, P.O. Box 248046, University of Miami, Coral Gables, FL 33124 USA ar X iv :0 90 1. 33 34 v2 [ he pth ] 2 8 Ja n 20 09