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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.Comment: 17 pages, paper to be published in Frontiers in Physic
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