Non-split and split deformations of AdS_5

TL;DR

This paper explores various split and non-split r matrices in AdS_5 deformations, analyzing their geometries, limits, supergravity backgrounds, and S-matrices, revealing their interrelations and extensions to AdS_5 x S^5.

Contribution

It systematically studies different r matrices in AdS_5 deformations, extending them to AdS_5 x S^5 and analyzing their S-matrices and geometric properties.

Findings

Different r matrices lead to distinct geometries and S-matrices.

The S-matrices are related by momentum-dependent basis transformations.

Extensions to AdS_5 x S^5 preserve key deformation features.

Abstract

The eta-deformation of the AdS_5 x S^5 superstring depends on a non-split r matrix for the superalgebra psu(2,2|4). 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 su(2,2), the isometry algebra of AdS_5, 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 AdS_5 x S^5 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.