L. Borsten, M. J. Duff, S. Ferrara, A. Marrani
Freudenthal duality (F-duality) was originally introduced as a non-polynomial anti-involution acting on the electromagnetic charges carried by extremal black hole solutions in the broad class of supergravity theories with U-duality groups of type E7. In this context F-duality is a symmetry of the Bekenstein-Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions, but also of the equations of motion themselves. A further role for F-duality is introduced in the context of world-sheet actions. The Nambu-Goto world-sheet action in any (t, s) signature spacetime can be written in terms of the F-dual. The corresponding field equations and Bianchi identities are then related by F-duality allowing for an F-dual formulation of Gaillard-Zumino duality on the world-sheet. An equivalent polynomial "Polyakov-type" action is introduced using the so-called black hole potential. Such a construction allows for actions invariant under all groups of type E7, including E7 itself, although in this case the stringy interpretation is less clear.
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http://arxiv.org/abs/1212.3254
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