Abstract
Freudenthal duality in N = 2, D = 4 ungauged supergravity is generated by an anti-involutive operator that acts on the electromagnetic fluxes, and results to be a symmetry of the Bekenstein-Hawking entropy. We show that, with a suitable extension, this duality can be generalized to the abelian gauged case as well, even in presence of hypermultiplets. By defining Freudenthal duality along the scalar flow, one can prove that two configurations of charges and gaugings linked by the Freudenthal operator share the same set of values of the scalar fields at the black hole horizon. Consequently, Freudenthal duality is promoted to a nonlinear symmetry of the black hole entropy. We explicitly show this invariance for the model with prepotential F = −iX0X1 and Fayet-Iliopoulos gauging.
Highlights
Freudenthal duality in N = 2, D = 4 ungauged supergravity is generated by an anti-involutive operator that acts on the electromagnetic fluxes, and results to be a symmetry of the Bekenstein-Hawking entropy
Freudenthal duality is promoted to a nonlinear symmetry of the black hole entropy
JHEP04(2017)013 known solutions of ungauged theories, further advances were made in [20], where the gauged supergravity analogue of the BPS attractor equations for theories coupled to hypermultiplets are derived and black holes with running hyperscalars are obtained numerically
Summary
The attractor mechanism [1,2,3,4,5] essentially states that, at the horizon of an extremal black hole, the scalar fields φ of the theory are always attracted to the same values φh (fixed by the black hole charges Q), independently of their values φ∞ at infinity. The Bekenstein-Hawking entropy turns out to be independent of these unstabilized moduli Notice that this does not hold anymore for nonextremal black holes, for which the horizon is not necessarily an attractor point. The φh are critical points of the black hole potential VBH(Q, zi), where in N = 2, D = 4 supergravity the zi denote only the scalars in the vector multiplets, since hypermultiplets can be consistently decoupled. Correctly the black hole potential that governs the attractor mechanism in ungauged supergravity. The fact that this limit does not exist for κ = 0, −1 is not surprising since flat or hyperbolic horizon geometries are incompatible with vanishing scalar potential.
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