S-matrix for magnons in the D1-D5 system

TL;DR

The paper shows that the magnon S-matrix for excitations in the D1-D5 AdS3×S3 system is fixed by SU(1|1)×SU(1|1) symmetry up to a scalar phase. It computes the leading strong-coupling phase from semiclassical giant-magnon solutions, and then determines the one-loop correction to the phase via bosonic and fermionic fluctuations using dressing and finite-gap methods. The authors verify crossing- and unitarity-consistency conditions at one loop and demonstrate that the magnon dispersion is one-loop exact at strong coupling, consistent with BPS protection. The work also interprets the phase in the context of potential all-coupling Bethe equations and nontrivial coproducts, highlighting the integrable structure of AdS3/CFT2 in the D1-D5 system.

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.