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

TL;DR

This paper performs a two-loop calculation of the S-matrix in N=6 Chern-Simons theory, confirming the weak-coupling limit of the proposed all-loop S-matrix and demonstrating reflectionless scattering of particle types.

Contribution

It provides the first direct coordinate Bethe ansatz computation of the two-loop S-matrix in ABJM theory, validating the all-loop S-matrix proposal at weak coupling.

Findings

Two-loop S-matrix matches the weak-coupling limit of the all-loop S-matrix.

Scattering of A and B particles is reflectionless.

Comparison with N=4 SYM one-loop S-matrix highlights similarities.

Abstract

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.