Worldsheet scattering in AdS(3)/CFT(2)

TL;DR

This paper compares exact S-matrix proposals for AdS(3)/CFT(2) with direct worldsheet calculations, finding good agreement at tree level but discrepancies at one-loop, and testing proposed phase modifications.

Contribution

It provides the first detailed comparison between exact S-matrices and worldsheet scattering amplitudes in AdS(3)/CFT(2), including one-loop corrections and phase modifications.

Findings

Tree-level amplitudes agree well with exact S-matrix predictions.

One-loop calculations reveal discrepancies due to non-visible processes.

A proposed phase modification accurately reproduces worldsheet results.

Abstract

We confront the recently proposed exact S-matrices for AdS(3)/CFT(2) with direct worldsheet calculations. Utilizing the BMN and Near Flat Space (NFS) expansions for strings on AdS(3) x S(3) x S(3) x S(1) and AdS(3) x S(3) x T(4) we compute both tree-level and one-loop scattering amplitudes. Up to some minor issues we find nice agreement in the tree-level sector. At the one-loop level however we find that certain non-zero tree-level processes, which are not visible in the exact solution, contribute, via the optical theorem, and give an apparent mismatch for certain amplitudes. Furthermore we find that a proposed one-loop modification of the dressing phase correctly reproduces the worldsheet calculation while the standard Hernandez-Lopez phase does not. We also compute several massless to massless processes.