Non-split and split deformations of

Abstract

The η deformation of the superstring depends on a non-split r matrix for the superalgebra . Much of the investigation into this model has considered one particular choice, however there are a number of inequivalent alternatives. This is also true for the bosonic sector of the theory with , the isometry algebra of , admitting one split and three non-split r matrices. In this article we explore these r matrices and the corresponding geometries. We investigate their contraction limits, comment on supergravity backgrounds and demonstrate their relation to gauged-WZW deformations. We then extend the three non-split cases to and compute four separate bosonic two-particle tree-level S-matrices based on inequivalent BMN-type light-cone gauges. The resulting S-matrices, while different, are related by momentum-dependent one-particle changes of basis.