Yannick Zimmermann (HU Berlin)

Title: Solving puzzles of η-deformed AdS₅⨉S⁵

Abstract:

Integrable models play a major role in the exploration of the AdS/CFT correspondence. The canonical example on the string theory side is the superstring on AdS₅⨉S⁵, a maximally supersymmetric sigma model. In the attempt of extending the correspondence to less symmetric theories, the big class of integrable Yang-Baxter deformations has received a lot of attention. The individual deformed models have distinct algebraic characteristics and interpretations in terms of string theory and AdS/CFT.

In this talk I will focus on so-called η (or inhomogeneous) Yang-Baxter deformations, which algebraically correspond to trigonometric quantum deformations of the symmetry group. Whereas their classical theory is well understood, an initial study of the quantum theory by Arutyunov, Borsato and Frolov (2015) led to puzzling results. It seemed that the classical integrability and symmetries do not transfer to the quantum theory. Furthermore the background of the model does not satisfy the supergravity equations of motion, essential for the Weyl invariance of the superstring model.

The discovery of another η deformation, this time providing a supergravity solution, sparked hope that it could resolve the issues of the former model. This talk will be about the analysis of this second deformation. In particular we (1) calculated the perturbative tree-level S matrix of worldsheet excitations, (2) tested it against the Yang-Baxter equation and (3) compared it to the exact S matrix derived from the quantum-deformed symmetry algebra. All these checks for the second deformation pass successfully, resolving the issues found in the first study. This strengthens the case that the superstring on η-deformed AdS₅⨉S⁵ is quantum integrable and has quantum-deformed psu_q(2,2|4) symmetry.

This is joint work together with Fiona Seibold and Stijn van Tongeren.