Black holes and general Freudenthal transformations

L. Borsten, M. J. Duff, J. J. Fernández-Melgarejo, A. Marrani, E. Torrente-Lujan

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We study General Freudenthal Transformations (GFT) on black hole solutions in Einstein-Maxwell-Scalar (super)gravity theories with global symmetry of type E7. GFT can be considered as a 2-parameter, a, b ∈ ℝ, generalisation of Freudenthal duality: x→ xF= ax+ bx˜ , where x is the vector of the electromagnetic charges, an element of a Freudenthal triple system (FTS), carried by a large black hole and x˜ is its Freudenthal dual. These transformations leave the Bekenstein-Hawking entropy invariant up to a scalar factor given by a2 ± b2. For any x there exists a one parameter subset of GFT that leave the entropy invariant, a2 ± b2 = 1, defining the subgroup of Freudenthal rotations. The Freudenthal plane defined by span{x,x˜ } is closed under GFT and is foliated by the orbits of the Freudenthal rotations. Having introduced the basic definitions and presented their properties in detail, we consider the relation of GFT to the global symmetries or U-dualities in the context of supergravity. We consider explicit examples in pure supergravity, axion-dilaton theories and N = 2, D = 4 supergravities obtained from D = 5 by dimensional reductions associated to (non-degenerate) reduced FTS’s descending from cubic Jordan Algebras.

Original languageEnglish
Article number70
JournalJournal of High Energy Physics (JHEP)
Issue number7
Publication statusPublished - 1 Jul 2019


  • Black Holes
  • Supergravity Models
  • Supersymmetry and Duality


Dive into the research topics of 'Black holes and general Freudenthal transformations'. Together they form a unique fingerprint.

Cite this