TY - JOUR

T1 - Black holes and general Freudenthal transformations

AU - Borsten, L.

AU - Duff, M. J.

AU - Fernández-Melgarejo, J. J.

AU - Marrani, A.

AU - Torrente-Lujan, E.

N1 - Publisher Copyright:
© 2019, The Author(s).

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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 spanℝ{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.

AB - 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 spanℝ{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.

KW - Black Holes

KW - Supergravity Models

KW - Supersymmetry and Duality

UR - http://www.scopus.com/inward/record.url?scp=85068939226&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2019)070

DO - 10.1007/JHEP07(2019)070

M3 - Article

AN - SCOPUS:85068939226

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 70

ER -