Scattering in AdS(2)/CFT(1) and the BES Phase

TL;DR

This paper investigates worldsheet scattering in AdS(2) x S(2) x T(6) superstring theory, computing tree-level and one-loop S-matrices, and finds evidence that the all-loop dressing phase is the BES phase, similar to higher-dimensional cases.

Contribution

It provides the first detailed computation of scattering amplitudes in AdS(2)/CFT(1), demonstrating the universality of the BES phase across different AdS/CFT setups.

Findings

Tree-level scattering matrices match truncated AdS(5) x S(5) results.

One-loop dressing phase is the Hernandes-Lopez phase.

Supports the conjecture that the all-loop phase is the BES phase.

Abstract

We study worldsheet scattering for the type IIA superstring in AdS(2) x S(2) x T(6). Using the Green--Schwarz action to quartic order in fermions we take the near-BMN limit, where as in the AdS(3)/CFT(2) case there are both massive and massless excitations. For the massive excitations we compute all possible tree-level processes, and show that these agree with a truncated version of the exact AdS(5) x S(5) S-matrix. We also compute several S-matrix elements involving massless excitations. At one loop we find that the dressing phase is the same Hernandes-Lopez phase appearing in AdS(5)/CFT(4). We see the same phase when calculating this by semiclassical means using the PSU(1,1|2)/U(1)^2 coset sigma model, for which we can also study the scattering of fermions. This supports the conjecture that the all-loop dressing phase is again the BES phase, rather than a new phase like that seen in AdS(3)/CFT(2).