Non-abelian T-duality and Applications in String Theory
Summary
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.