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arXiv · 1212.3254

Freudenthal Dual Lagrangians

L. Borsten·M. J. Duff·S. Ferrara·A. Marrani
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Abstract

The global U-dualities of extended supergravity have played a central role in differentiating the distinct classes of extremal black hole solutions. When the U-duality group satisfies certain algebraic conditions, as is the case for a broad class of supergravities, the extremal black holes enjoy a further symmetry known as Freudenthal duality (F-duality), which although distinct from U-duality preserves 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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L. Borsten, M. J. Duff, S. Ferrara, A. Marrani. 2013-10-10. Freudenthal Dual Lagrangians. https://doi.org/10.1088/0264-9381%2F30%2F23%2F235003

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