New Reflections on Gravitational Duality

In general terms duality consists of two descriptions of one physical system by using degrees of freedom of different nature. There are different kinds of dualities and they have been extremely useful to uncover the underlying strong coupling dynamics of gauge theories in various dimensions and those of the diverse string theories. Perhaps the oldest example exhibiting this property is Maxwell theory, which interchanges electric and magnetic fields. An extension of this duality involving the sources is also possible if the magnetic monopole is incorporated. At the present time a lot has been understood about duality in non-abelian gauge theories as in the case of N = 4 supersymmetric gauge theories in four dimensions or in the Seiberg-Witten duality for N = 2 theories. Moreover, a duality that relates a gravitational theory (or a string theory) and a conformal gauge theory, as in the case of gauge/gravity correspondence, have been also studied with considerable detail. The case of duality between two gravitational theories is the so called gravitational duality. At the present time, this duality has not been exhaustively studied, however some advances have been reported in the literature. In the present paper we give a general overview of this subject. In particular we will focus on non-abelian dualities, applied to various theories of gravity as developed by the authors, based in the Rocek-Verlinde duality procedure. Finally, as a new development in this direction, we study the gravitational duality in Hitchin's gravity in seven and six dimensions and their relation is also discussed.