Unitary supermultiplets of and the AdS7/CFT6 duality

Günaydın, Murat; Takemae, Seiji

doi:10.1016/s0550-3213(00)00026-2

Cited by 31 publications

(35 citation statements)

References 42 publications

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“…In [18] it was shown explicitly how to go from the compact U(4) particle basis of the ULWR's of SO * (8) to the non-compact SU * (4) × SO(1, 1) coherent state basis. ( SU * (4) × SO(1, 1) is simply the covering group of the Lorentz group in six dimensions times dilatations) .…”

Section: Covariant Quantum Fields Over Generalized Spacetimes and Thementioning

confidence: 99%

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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: Covariant Quantum Fields Over Generalized Spacetimes and Thementioning

confidence: 99%

“…As was done explicitly for the conformal groups in 4 and 6 dimensions [17,18] one can show that there exists a rotation operator W in the representation space with the property that the states W |Ω are annihilated by all the generators belonging to n − n − W |Ω = 0…”

Section: Covariant Quantum Fields Over Generalized Spacetimes and Thementioning

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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“…Similarly, the conformal group SO * (8) of the Jordan algebra J H 2 parametrizing the six dimensional Minkowski space has a maximal compact subgroup U(4) which is the compact form of the structure group SU * (4) × SO(1, 1). In [22] it was shown how to go from the compact U(4) basis of the ULWR's of SO * (8) to the non-compact basis SU * (4) × SO(1, 1) which is simply the Lorentz group in six dimensions times dilatations. The coherent states of the non-compact basis are again labelled by the elements of the Jordan algebra J H 2 of 2×2 hermitian quaternionic matrices representing the coordinates of 6d Minkowski space.…”

Section: Conformal Fields Over Generalized Spacetimes and The Positivmentioning

confidence: 99%

“…These representations have been called " doubletons" since they require two sets of oscillators for their realization [10,12]. The doubleton supermultiplets of extended AdS supergroups in d = 5 (SU(2, 2/N)) and d = 7 (OSp(8 * /2N)) share the same remarkable features of the singleton supermultiplets of d = 4 AdS supergroups i.e the tensor product of any two doubletons decompose into an infinite set of massless supermultiplets [10,12,19,20,21,22]. In d = 3 the AdS group SO(2, 2) is not simple and is isomorphic to SO(2, 1) × SO(2, 1).…”

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confidence: 99%

“…The tensor product of more than two copies of the singleton or doubleton supermultiplets of AdS supergroups decompose into an infinite set of massive supermultiplets [10,9,12,6,20,21,22,24,25,26,27] . The KaluzaKlein spectrum of the 11-dimensional and ten dimensional IIB supergravity compactified over S 7 (S 4 ) and S 5 fall into CPT self-conjugate short massless and massive supermultiplets of OSp(8|4, R)(OSp(8 * |4)) and SU(2, 2|4), respectively.…”

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confidence: 99%

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GENERALIZED ADS/CFT DUALITIES AND SPACE-TIME SYMMETRIES OF M/SUPERSTRING THEORY

Günaydın

2002

The Ninth Marcel Grossmann Meeting

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I review the relationship between AdS/CFT ( anti-de Sitter / conformal field theory) dualities and the general theory of unitary lowest weight (ULWR) (positive energy) representations of non-compact space-time groups and supergroups. The ULWR's have the remarkable property that they can be constructed by tensoring some fundamental ULWR's ( singletons or doubletons). Furthermore, one can go from the manifestly unitary compact basis of the ULWR's of the conformal group ( Wigner picture) to the manifestly covariant coherent state basis ( Dirac picture) labelled by the space-time coordinates. Hence every irreducible ULWR corresponds to a covariant field with a definite conformal dimension. These results extend to higher dimensional generalized spacetimes ( superspaces) defined by Jordan (super) algebras and Jordan (super) triple systems. In particular, they extend to the ULWR's of the M-theory symmetry superalgebra OSp(1/32, R).

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Lectures on Branes, Black Holes, and Anti-de Sitter Space

Duff¹

2002

Theoretical Physics at the End of the Twentieth Century

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Unitary supermultiplets of and the AdS7/CFT6 duality

Cited by 31 publications

References 42 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

GENERALIZED ADS/CFT DUALITIES AND SPACE-TIME SYMMETRIES OF M/SUPERSTRING THEORY

Lectures on Branes, Black Holes, and Anti-de Sitter Space

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