Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory

TL;DR

This paper explores how homogeneous Yang-Baxter deformations of the AdS_5 x S^5 superstring relate to noncommutative gauge theories, introducing novel jordanian deformations and their potential dual gauge theories via brane constructions.

Contribution

It provides a new interpretation of homogeneous Yang-Baxter deformations as noncommutative gauge theories, especially focusing on jordanian types and their symmetry structures.

Findings

Jordanian deformations are novel and have distinct gauge duals.

Brane constructions support the conjectured duality for specific jordanian examples.

Discussion of kappa-Minkowski deformations as potential duals.

Abstract

We give an AdS/CFT interpretation to homogeneous Yang-Baxter deformations of the AdS_5 x S^5 superstring as noncommutative deformations of the dual gauge theory, going well beyond the canonical noncommutative case. These homogeneous Yang-Baxter deformations can be of so-called abelian or jordanian type. While abelian deformations have a clear interpretation in string theory and many already had well understood gauge theory duals, jordanian deformations appear novel on both counts. We discuss the symmetry structure of the deformed string from the uniformizing perspective of Drinfeld twists and indicate that this structure can be realized on the gauge theory side by considering theories on various noncommutative spaces. We then conjecture that these are the gauge theory duals of our strings, modulo subtleties involving singularities. We support this conjecture by a brane construction for two jordanian examples, corresponding to noncommutative spaces with [x^-,x^i] ~ x^i (i=1,2). We also discuss kappa-Minkowski type deformations of AdS_5 x S^5, one of which may be the gravity dual of gauge theory on spacelike kappa-Minkowski space.