Non-abelian T-duality and Applications in String Theory

Abstract

Target space duality (T-duality) is a nontrivial transformation between compactified string theory backgrounds that leave the physics invariant. It is characterized by the inversion of the length scale and the exchange of tangent and cotangent components of string momenta and it is described accurately in the language of generalized geometry. The cases where the isometry group of the internal manifold is non-Abelian carries the name non-Abelian T-duality. Abelian T-duality can be interpreted as an equivalence of Courant algebroids over torus bundles, but a comparable formalism of non-Abelian T-duality is lacking. In this work, we study two non-Abelian T-duality frameworks, called Poisson-Lie T-duality and topological spherical T-duality. We compute explicitly Poisson-Lie T-dual backgrounds and propose an interpretation of Poisson-Lie T-duality in generalized geometry. Finally, we develop an uncomplicated formalism of spherical T-duality directly from Abelian T-duality and derive an equivalence of twisted cohomologies of spherical T-duals where we allow for a difference in dimension.