Supersymmetric black holes and Freudenthal duality

Marrani, Alessio; Mandal, Taniya; Tripathy, Prasanta Kumar

doi:10.1142/s0217751x17501147

Cited by 9 publications

(7 citation statements)

References 30 publications

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“…refs. therein, as well), as well as of the non-homogeneous 2-moduli cubic models in which non-trivial involutory matrices determining multiple attractor solutions exist [98,103]; we leave these tasks for further future work.…”

Section: Jhep12(2021)195mentioning

confidence: 99%

BPS black hole entropy and attractors in very special geometry. Cubic forms, gradient maps and their inversion

Geemen

Alessio

Francesco

2021

J. High Energ. Phys.

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We consider Bekenstein-Hawking entropy and attractors in extremal BPS black holes of $$ \mathcal{N} $$ N = 2, D = 4 ungauged supergravity obtained as reduction of minimal, matter-coupled D = 5 supergravity. They are generally expressed in terms of solutions to an inhomogeneous system of coupled quadratic equations, named BPS system, depending on the cubic prepotential as well as on the electric-magnetic fluxes in the extremal black hole background. Focussing on homogeneous non-symmetric scalar manifolds (whose classification is known in terms of L(q, P, Ṗ) models), under certain assumptions on the Clifford matrices pertaining to the related cubic prepotential, we formulate and prove an invertibility condition for the gradient map of the corresponding cubic form (to have a birational inverse map which is given by homogeneous polynomials of degree four), and therefore for the solutions to the BPS system to be explicitly determined, in turn providing novel, explicit expressions for the BPS black hole entropy and the related attractors as solution of the BPS attractor equations. After a general treatment, we present a number of explicit examples with Ṗ = 0, such as L(q, P), 1 ⩽ q ⩽ 3 and P ⩾ 1, or L(q, 1), 4 ⩽ q ⩽ 9, and one model with Ṗ = 1, namely L(4, 1, 1). We also briefly comment on Kleinian signatures and split algebras. In particular, we provide, for the first time, the explicit form of the BPS black hole entropy and of the related BPS attractors for the infinite class of L(1, P) P ⩾ 2 non-symmetric models of $$ \mathcal{N} $$ N = 2, D = 4 supergravity.

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Section: Jhep12(2021)195mentioning

confidence: 99%

BPS black hole entropy and attractors in very special geometry. Cubic forms, gradient maps and their inversion

Geemen

Alessio

Francesco

2021

J. High Energ. Phys.

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“…where ∆ a = D abc xb xc = 3D abc p b p c − p 0 q a with real xa . Following [36], one can write the above expression as…”

Section: Brief Review Of N = Supergravity and F-dualitymentioning

confidence: 99%

“…It has been shown in [36] that D0 − D2 − D4 − D6 black hole has a Freudenthal dual black with charge configuration D0 − D4 − D6. One can further show that a STU D0 − D2 − D4 − D6 black hole can also be F-dual to another D0 − D2 − D4 − D6 black hole.…”

Section: Near Extremal Entropymentioning

confidence: 99%

“…In [36], it has been explicitly shown that for N = 2, IIA supergravity, an extremal supersymmetric D0−D4−D6 black hole is Freudenthal dual to an extremal supersymmetric D0 − D2 − D4 − D6 black hole. Freudenthal duality has also been studied in the context of N > 2 supergravities [30].…”

mentioning

confidence: 99%

“…symplectic matrix with Ω T = −Ω and Ω 2 = −I.Thus by F-dualizing an extremal D0 − D2 − D4 − D6 supersymmetric black hole, one would expect to get another extremal D0 − D2 − D4 − D6 supersymmetric black hole whose charges non-linearly depend on that of the former one. Nevertheless, an extremal D0 − D2 − D4 − D6 supersymmetric black hole can also be mapped to an extremal D0 − D4 − D6 supersymmetric black hole via F-duality[36].…”

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Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity

Chattopadhyay,

Mandal

2021

Preprint

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Freudenthal duality (F-duality), an anti-involution of charge vectors keep the entropy and attractor solutions invariant for an extremal supersymmetric black hole. In this paper, we analyze the effect of F-duality on the entropy of a near-extremal ST U black hole in N = 2 ungauged, four-dimensional supergravity. We consider doubleextremal black holes, whose attractor solutions are fixed in terms of the black hole charges throughout the moduli space. It is well known that JT gravity governs the dynamics of the near-horizon regions of higher dimensional, near-extremal black holes. Owing to this fact, we reduce the four-dimensional supergravity theory to two dimensions to construct a Jackiw-Teitelboim (JT) gravity like model and compute the near-extremal entropy. We then analyze the effect of F-duality on this entropy.We show that the F-duality breaks down for the case of near-extremal solutions if one considers the duality operation generated through near-extremal entropy rather than the extremal one.

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Non-linear Symmetries in Maxwell-Einstein Gravity: From Freudenthal Duality to Pre-homogeneous Vector Spaces

Marrani

2020

Springer Proceedings in Mathematics &Amp; Statistics

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Supersymmetric black holes and Freudenthal duality

Cited by 9 publications

References 30 publications

BPS black hole entropy and attractors in very special geometry. Cubic forms, gradient maps and their inversion

BPS black hole entropy and attractors in very special geometry. Cubic forms, gradient maps and their inversion

Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity

Non-linear Symmetries in Maxwell-Einstein Gravity: From Freudenthal Duality to Pre-homogeneous Vector Spaces

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