Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2015-08

Stijn van Tongeren


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


Abstract: We discuss the AdS/CFT interpretation of homogeneous Yang-Baxter deformations of the AdS_5×S⁵ 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 show how it 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 time and singularities. We support this conjecture by a brane construction for two nontrivial examples, corresponding to noncommutative spaces with [x^- , x^i] ~ x^i (i=1,2). We also briefly discuss a deformation which may be the gravity dual of gauge theory on spacelike κ-Minkowski space.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2015-08


31 pp.