Real forms of non-linear superconformal and quasi-superconformal algebras and their unified realization

Bina, Behzad; Günaydın, Murat

doi:10.1016/s0550-3213(97)00406-9

Cited by 22 publications

(56 citation statements)

References 49 publications

(68 reference statements)

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“…This unified construction follows closely the formalism of unified construction of nonlinear superconformal and quasi-superconformal algebras in two dimensions [29]. The realization of the distinguished SL(2, R) subgroup generated by the grade ±2 elements in the unified construction is always of the form that arises in conformal or superconformal quantum mechanics.…”

Section: Discussionmentioning

confidence: 88%

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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Section: Discussionmentioning

confidence: 88%

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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“…While there appears to be no linear Lie algebra with this property (and no finite dimensional Lie superalgebra, either), an infinite dimensional non-linear algebra of W-type does exist. It is a nonlinear quasi-super conformal algebra denoted as Q©?8(8) [4]. The quasi-superconformal algebras in two dimensions were first introduced in [32] and further systematized in [3].…”

Section: Discussionmentioning

confidence: 99%

“…A classification of complex forms of quasi-superconformal algebras was given in [15]. In [4] a complete classification and a unified realization of the real forms of quasi-superconformal algebras were given.…”

Section: Discussionmentioning

confidence: 99%

“…The realization of Q-E^s) given in [4] involves 56 dimension 1/2 bosons and a dilaton, which leads to a realization of #8 (8) in the infinite central charge limit. It will be important to understand if the resulting realization can be related to the one given here.…”

Section: Discussionmentioning

confidence: 99%

“…That work evolved from an earlier attempt to determine the i? 4 corrections directly from the supermembrane and to understand them in terms of so-called "theta-correspondences" [31]; see also [34] for a related attempt to come to grips with the non-linearities of the supermembrane.…”

Section: And)£] =mentioning

confidence: 99%

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The minimal unitary representation of $E_{8(8)}$

Günaydın¹,

Koepsell²,

Nicolai³

2001

Advances in Theoretical and Mathematical Physics

122

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Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity

Henneaux¹,

Maoz²,

Schwimmer³

2000

Annals of Physics

158

277

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We investigate systematically the asymptotic dynamics and symmetries of all three-dimensional extended AdS supergravity models. First, starting from the Chern Simons formulation, we show explicitly that the (super)anti-de Sitter boundary conditions imply that the asymptotic symmetry algebra is the extended superconformal algebra with quadratic nonlinearies in the currents. We then derive the super-Liouville action by solving the Chern Simons theory and obtain a realization of the superconformal algebras in terms of super-Liouville fields. Finally, we discuss the possible periodic conditions that can be imposed on the generators of the algebra and generalize the spectral flow analysed previously in the context of the N-extended linear superconformal algebras with N 4. The (2+1)-AdSÂ2-CFT correspondence sheds a new light on the properties of the nonlinear superconformal algebras. It also provides a general and natural interpretation of the spectral flow. Academic Press

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Real forms of non-linear superconformal and quasi-superconformal algebras and their unified realization

Cited by 22 publications

References 49 publications

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

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

The minimal unitary representation of $E_{8(8)}$

Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity

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