# Abelian and non-Abelian T-duality

What are the advantages and the troubles of performing an Abelian and a non-Abelian T-duality over a type IIB/IIA solution? I have seen that Maldacena and Alday found some correspondence between the 4-point gluon scattering and the Wilson loop after T-dualised the geometry, for instance. However, I would like to understand better the idea and motivation behind the (Abelian/non-Abelian)T-duality and also the problems or the unclear things. One possible problem is the fact that T-duality is a symmetry at the order of perturbation string theory, why?

• $\uparrow$ Seen where? – Qmechanic Apr 21 '15 at 22:44

I have used T duality as a generating technique. When you apply the T-duality transformation (both Abelian and non-Abelian) rules to a IIA/IIB SUGRA background with Abelian or non-Abelian isometry, you obtain another solution in IIB/IIA respectively. That was the motivation in my studies, but certainly it is not the only. The main interest of dualities in general is the ability to relate string Physics in two different backgrounds, being the canonical instance the relation between two cylinders of radii $R$ and $1/R$ for Abelian duality.