Unified Maxwell-Einstein and Yang-Mills-Einstein supergravity theories in five dimensions

Günaydın, Murat; Zagermann, Marco

doi:10.1088/1126-6708/2003/07/023

Cited by 34 publications

(116 citation statements)

References 50 publications

(123 reference statements)

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“…In [71] it was shown that the N = 2, d = 5 "magical" MESGTs defined by J [27] and of the present work to these theories in five dimensions and to their descendants in four dimensions, respectively.…”

Section: Resultsmentioning

confidence: 75%

Charge Orbits of Symmetric Special Geometries and Attractors

Bellucci

Ferrara

Günaydın

et al. 2006

Int. J. Mod. Phys. A

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152

409

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We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 supergravity coupled to n V vector multiplets, in an asymptotically flat extremal black hole background described by a 2 (n V + 1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold.For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with non-vanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2 (n V + 1)-dimensional representation R V of the U-duality group. Such orbits are non-degenerate, namely they have non-vanishing quartic invariant (for rank-3 spaces). Other than the 1 2 -BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge.The three species of solutions to the N = 2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of V BH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

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Section: Resultsmentioning

confidence: 75%

Charge Orbits of Symmetric Special Geometries and Attractors

Bellucci

Ferrara

Günaydın

et al. 2006

Int. J. Mod. Phys. A

Self Cite

152

409

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show abstract

“…Of all the N = 2 MESGT's whose scalar manifolds are symmetric spaces only four are unified [5]. More recently it was shown that if one relaxes the condition that the scalar manifolds be homogeneous spaces then one finds three novel infinite families ( plus an additional sporadic one ) of unified MESGT's in d = 5 [6]. If one defines a cubic form…”

Section: U-duality Groups In Matter Coupled Supergravity Theoriesmentioning

confidence: 99%

Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories

Günaydın

2005

AIP Conference Proceedings

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We review the current status of the construction of unitary representations of Uduality groups of supergravity theories in five, four and three dimensions. We focus mainly on the maximal N = 8 supergravity theories and on the N = 2 MaxwellEinstein supergravity (MESGT) theories defined by Jordan algebras of degree three in five dimensions and their descendants in four and three dimensions. Entropies of the extremal black hole solutions of these theories in five and four dimensions are given by certain invariants of their U-duality groups. The five dimensional U-duality groups admit extensions to spectrum generating generalized conformal groups which are isomorphic to the U-duality groups of corresponding four dimensional theories. Similarly, the U-duality groups of four dimensional theories admit extensions to spectrum generating quasiconformal groups that are isomorphic to the corresponding Uduality groups in three dimensions. For example, the group E 8(8) can be realized as a quasiconformal group in the 57 dimensional charge-entropy space of BPS black hole solutions of maximal N = 8 supergravity in four dimensions and leaves invariant "lightlike separations" with respect to a quartic norm. Similarly E 7(7) acts as a generalized conformal group in the 27 dimensional charge space of BPS black hole solutions in five dimensional N = 8 supergravity and leaves invariant "lightlike separations" with respect to a cubic norm. For the exceptional N = 2 Maxwell-Einstein supergravity theory the corresponding quasiconformal and conformal groups are E 8(−24) and E 7(−25) , respectively. We outline the oscillator construction of the unitary representations of generalized conformal groups that admit positive energy representations, which include the U-duality groups of N = 2 MESGT's in four dimensions . We conclude with a review of the minimal unitary realizations of U-duality groups that are obtained by quantizations of their quasiconformal actions and discuss in detail the minimal unitary realization of E 8(8) .

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“…After [65][66][67], it is known that the Maxwell-Einstein supergravity theories based on such Jordan algebras have non-homogeneous vector multiplets' scalar manifolds. One could use J 2,1 (T) ∼ = J 1,2 (T) and J 2,1 (S) ∼ = J 1,2 (S) to construct theories in D = 4 and 5 dimensions, in the spirit of [65][66][67]. Again, these would not be supersymmetric, but would nonetheless share many features with magic supergravities.…”

Section: Discussionmentioning

confidence: 99%

A kind of magic

Borsten¹,

Marrani²

2017

Class. Quantum Grav.

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We introduce the extended Freudenthal-Rosenfeld-Tits magic square based on six algebras: the reals R, complexes C, ternions T, quaternions H, sextonions S and octonions O. The sextonionic row/column of the magic square appeared previously and was shown to yield the non-reductive Lie algebras, sp , for R, C, T, H, S and O respectively. The fractional ranks here are used to denote the semi-direct extension of the semi-simple Lie algebra in question by a unique (up to equivalence) nilpotent "Jordan" algebra. We present all possible real forms of the extended magic square. It is demonstrated that the algebras of the extended magic square appear quite naturally as the symmetries of supergravity Lagrangians. The sextonionic row (for appropriate choices of real forms) gives the noncompact global symmetries of the Lagrangian for the D = 3 maximal N = 16, magic N = 4 and magic non-supersymmetric theories, obtained by dimensionally reducing the D = 4 parent theories on a circle, with the graviphoton left undualised. In particular, the extremal intermediate non-reductive Lie algebrã e 7(7) 1 2 (which is not a subalgebra of e 8(8) ) is the non-compact global symmetry algebra of D = 3, N = 16 supergravity as obtained by dimensionally reducing D = 4, N = 8 supergravity with e 7(7) symmetry on a circle. On the other hand, the ternionic row (for appropriate choices of real forms) gives the non-compact global symmetries of the Lagrangian for the D = 4 maximal N = 8, magic N = 2 and magic nonsupersymmetric theories, as obtained by dimensionally reducing the parent D = 5 theories on a circle. In particular, the Kantor-Koecher-Tits intermediate non-reductive Lie algebra e 6(6) 1 4 is the non-compact global symmetry algebra of D = 4, N = 8 supergravity as obtained by dimensionally reducing D = 5, N = 8 supergravity with e 6(6) symmetry on a circle.

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Unified Maxwell-Einstein and Yang-Mills-Einstein supergravity theories in five dimensions

Cited by 34 publications

References 50 publications

Charge Orbits of Symmetric Special Geometries and Attractors

Charge Orbits of Symmetric Special Geometries and Attractors

Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories

A kind of magic

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