Integrable S-matrices, massive and massless modes and the AdS 2 × S 2 superstring

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 × S 2 × 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.

The AdS n × S n × T 10−2n BMN string at two loops

“…For AdS 2 × S 2 × T 6 the symmetries are not enough to completely fix the form of the dispersion relation [32] but nevertheless we find the same two-loop correction as for the other cases but with g replaced by 2g (the same was observed at one loop in [21]). For the massless modes in AdS 3 × S 3 × T 4 the exact dispersion relation was suggested, based on a similar symmetry argument that gave the massive mode dispersion relation, to have the same form as in (1.2) except with the 1 in the first term replaced by 0 [31].…”

The full Quantum Spectral Curve for AdS4/CFT3

“…[47,[76][77][78]. These cases are less supersymmetric, and the construction may be expected to be even more complicated.…”

The AdS3× S3× S3× S1worldsheetSmatrix

“…As a result, they could be applied to other, less symmetric backgrounds, associated not just to less-symmetric cosets [77,78], but perhaps also to other AdS backgrounds such as [79][80][81][82][83]. While these latter backgrounds are not expected to be integrable, it would be interesting to establish what happens to the symmetry algebra of the gauge-fixed action when the level-matching condition is relaxed.…”