Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring

TL;DR

This paper derives the exact S-matrix for certain representations related to the massive and massless modes of the AdS_2 x S^2 superstring, exploring symmetry constraints and limits relevant for integrability.

Contribution

It provides the explicit form of the S-matrix for the AdS_2 x S^2 superstring, including symmetry analysis and massless limits, advancing understanding of integrable structures in this background.

Findings

Derived the exact S-matrix for the superstring modes.

Analyzed symmetry constraints including crossing and unitarity.

Explored massless limits and their implications for the full S-matrix.

Abstract

We derive the exact S-matrix for the scattering of particular representations of the centrally-extended psu(1|1)^2 Lie superalgebra, conjectured to be related to the massive modes of the light-cone gauge string theory on AdS_2 x S^2 x T^6. The S-matrix consists of two copies of a centrally-extended psu(1|1) invariant S-matrix and is in agreement with the tree-level result following from perturbation theory. Although the overall factor is left unfixed, the constraints following from crossing symmetry and unitarity are given. The scattering involves long representations of the symmetry algebra, and the relevant representation theory is studied in detail. We also discuss Yangian symmetry and find it has a standard form for a particular limit of the aforementioned representations. This has a natural interpretation as the massless limit, and we investigate the corresponding limits of the massive S-matrix. Under the assumption that the massless modes of the light-cone gauge string theory transform in these limiting representations, the resulting S-matrices would provide the building blocks for the full S-matrix. Finally, some brief comments are given on the Bethe ansatz.