Freudenthal Duality and Generalized Special Geometry

TL;DR

This paper proves that Freudenthal duality is a symmetry of black hole entropy and critical points in supergravity theories, extending its applicability to generalized special geometries beyond classical cases.

Contribution

It demonstrates that Freudenthal duality is a symmetry of black hole entropy and potential critical points, and extends its framework to all N > 2 supergravities and N=2 special geometries.

Findings

Freudenthal duality is a symmetry of classical Bekenstein-Hawking entropy.

It is also a symmetry of the critical points of the black hole potential.

The duality is extended to generalized special geometries, including all N > 2 supergravities.

Abstract

Freudenthal duality, introduced in L. Borsten, D. Dahanayake, M. J. Duff and W. Rubens, Phys.Rev. D80, 026003 (2009), and defined as an anti-involution on the dyonic charge vector in d = 4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential. Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N > 2 supergravities, as well as N = 2 generic special geometry, not necessarily having a coset space structure.