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

TL;DR

The paper investigates worldsheet scattering for the type IIA string on $AdS_2\times S^2\times T^6$ in the near-BMN limit to test the universality of the BES dressing phase in AdS/CFT with reduced supersymmetry. It builds the Green–Schwarz action to quartic order, separates massive coset modes from massless torus modes, and analyzes tree-level and one-loop amplitudes, complemented by a semiclassical coset-model calculation of the dressing phase. The authors find that the tree-level massive sector matches a truncated $AdS_5\times S^5$ S-matrix, and that the one-loop dressing phase agrees with the Hernandez–Lopez form, consistent with the BES phase when scaled by the appropriate coupling $h$, with the semiclassical result in agreement with the full worldsheet calculation. Massless modes, while affecting certain loop contributions and truncation schemes, do not undermine the HL/BES structure at one loop, as confirmed by near-flat-space analyses and optical-theorem checks. Overall, the work supports BES universality of the dressing phase in $AdS_2/CFT_1$ and clarifies the role of massless modes and truncations in this integrable setting.

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).