Integrable deformations and the AdS/CFT correspondence

Abstract

The purpose of this research project is to further explore the properties of the lambda model of the Green-Schwarz superstring in the $AdS_{5}\times S^{5}$ background. The lambda model is a deformation of the non-Abelian T-dual of the superstring sigma model action functional and preserves not only the integrability but also the quantum conformal symmetry of the later. This deformation has, recently, attracted a great deal of attention because it suggests the existence of a consistent $q$-deformation (with $q$ a root-of-unity) of the conventional AdS/CFT correspondence. We plan to explore some specific aspects of the lambda model like its affine quantum group symmetry structure, its relation to the Chern-Simons theories and its possible first-principle quantization scheme, the problem of the non-ultralocality thereof, the relation with its parent sigma model and how this remarkable integrable deformation might manifest itself on the gauge theory side of the gauge/gravity duality. (AU)