Hidden symmetries in string theory

Abstract

In this thesis we study hidden symmetries within the framework of string theory. Symmetries play a very important role in physics: they lead to drastic simplifications, which allow one to compute various physical quantities without relying on perturbative techniques.There are two kinds of hidden symmetries investigated in this work: the first type is associated with dynamics of quantum fields and the second type is related to integrability of strings on various backgrounds. Integrability is a remarkable property of some theories that allows one to determine all dynamical properties of the system using purely analytical methods. The goals of this thesis are twofold: extension of hidden symmetries known in General Relativity to stringy backgrounds in higher dimensions and construction of new integrable string theories.In the context of the first goal we study hidden symmetries of stringy backgrounds, with and without supersymmetry. For supersymmetric geometries produced by D-branes we identify the backgrounds with solvable equations for geodesics, which can potentially give rise to integrable string theories. Relaxing the requirement of supersymmetry, we also study charged black holes in higher dimensions and identify their hidden symmetries encoded in socalled Killing(-Yano) tensors. We construct the explicit form of the Killing(-Yano) tensors for the charged rotating black hole in arbitrary number of dimensions, study behavior of such tensors under string dualities, and use the analysis of hidden symmetries to explain why exact solutions for black rings (black holes with non-spherical event horizons) in more than five dimensions remain elusive. As a byproduct we identify the standard parameterization of AdS p × S q backgrounds with elliptic coordinates on a flat base.The second goal of this work is construction of new integrable string theories by applying continuous deformations of known examples. We use the recent developments called (generalized) λ-deformation to construct new integrable backgrounds depending on several continuous parameters and study analytical properties of the such deformations. C Appendix for Towards higher dimensional black rings C.1 Myers-Perry black holes and the neutral black ring . . . . . . . . . . . . . . D Appendix for Background of the λ-deformed AdS 3 × S 3 supercoset D.1 λ-deformation for AdS 2 ×S 2 . .