Worldsheet scattering in AdS(3)/CFT(2)
Per Sundin, Linus Wulff
TL;DR
This work tests proposed exact S-matrices for $AdS_3/CFT_2$ against explicit worldsheet computations in BMN and Near Flat Space expansions for strings on $AdS_3\times S^3\times S^3\times S^1$ and $AdS_3\times S^3\times T^4$. Tree-level scattering generally agrees with the $Borsato\text{–}Beisert$-type S-matrix once gauge-dependent phases are included, while amplitudes involving fermions disagree with the $Ahn$ proposal. At one loop, the real parts show mismatches traced to additional tree-level processes not captured by the proposed S-matrices, whereas the imaginary parts align when using the Beccaria et al. one-loop phase; the optical theorem clarifies how missing channels feed into loop results. The massless sector and the alpha-parameter dependence highlight subtle consistency conditions, suggesting the exact S-matrix must be refined to account for heavy modes becoming fundamental at the endpoints ($\alpha=0,1$). These findings inform the integrable structure of $AdS_3/CFT_2$ and guide future tests of proposed S-matrices and dressing phases.
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.