S-matrix for magnons in the D1-D5 system

TL;DR

This paper determines the magnon scattering matrix in the D1-D5 system's near horizon geometry using integrability and symmetry principles, and computes the phase factor at strong coupling.

Contribution

It provides the complete S-matrix for magnons in the D1-D5 system up to a phase, including explicit phase calculations at strong coupling and one-loop order.

Findings

Phase obeys unitarity and crossing symmetry at one-loop.

Dispersion relation is one-loop exact at strong coupling.

Results support the BPS nature of the magnons.

Abstract

We show that integrability and symmetries of the near horizon geometry of the D1-D5 system determine the S-matrix for the scattering of magnons with polarizations in AdS3 $\times$ S3 completely up to a phase. Using semi-classical methods we evaluate the phase to the leading and to the one-loop approximation in the strong coupling expansion. We then show that the phase obeys the unitarity constraint implied by the crossing relations to the one-loop order. We also verify that the dispersion relation obeyed by these magnons is one-loop exact at strong coupling which is consistent with their BPS nature.