Freudenthal Dual Lagrangians

TL;DR

This paper explores the role of Freudenthal duality in supergravity, showing it as a symmetry of black hole solutions and equations of motion, and introduces F-duality in world-sheet actions with implications for string theory.

Contribution

It demonstrates that Freudenthal duality is a symmetry of equations of motion in supergravity and extends its application to world-sheet actions, providing new invariant formulations.

Findings

F-duality preserves black hole entropy

F-duality is a symmetry of equations of motion

Invariant actions under E7 groups are constructed

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.