Abstract
Non-Abelian T-duality (NATD) is a solution generating transformation for supergravity backgrounds with non-Abelian isometries. We show that NATD can be de-scribed as a coordinate dependent O(d,d) transformation, where the dependence on the coordinates is determined by the structure constants of the Lie algebra associated with the isometry group. Besides making calculations significantly easier, this approach gives a natural embedding of NATD in Double Field Theory (DFT), a framework which provides an O(d,d) covariant formulation for effective string actions. As a result of this embedding, it becomes easy to prove that the NATD transformed backgrounds solve supergravity equations, when the isometry algebra is unimodular. If the isometry algebra is non-unimodular, the generalized dilaton field is forced to have a linear dependence on the dual coordinates, which implies that the resulting background solves generalized supergravity equations.
Highlights
A compact formula for the transformation of the supergravity fields for a generic Green-Schwarz string with isometry G has been obtained in [17], where they showed that the sigma model after Non-Abelian T-duality (NATD) has kappa symmetry
The dependence on the coordinates is determined by the structure constants of the Lie algebra associated with the isometry group
As a result of this embedding, we managed to prove that the NATD fields solve supergravity equations, when the isometry algebra is unimodular
Summary
Let g and B be the metric and the Kalb-Ramond 2-form field that describes a D dimensional supergravity background, with d commuting isometries. Let us decompose the background matrix with respect to this choice of coordinates as. Define (along with the transformed dilaton field we will discuss below, see (2.10)) valid supergravity backgrounds. The O(D, D, R) transformation defined above acts as a solution generating transformation. Let us write the final form of the transformed background matrix Q : E (a − E c)F 2. For the resulting background to be a valid supergravity solution, the dilaton field φ should transform under O(D, D, R) in the following way: e−2φ = e−2φ detG detG (2.10). It is checked from (2.10) that e−2d = e−2d under O(D, D).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
