Multiplet shortening in Osp(N,4)

Freedman, Daniel Z.; Nicolai, Hermann

doi:10.1016/0550-3213(84)90164-0

Cited by 112 publications

(81 citation statements)

References 23 publications

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“…The modes for other spin fields are determined by the fact that together with the graviton modes they must form unitary irreducible representations (UIR) of U(2,2/4). Since the highest spin field in the massive supermultiplets is s = 2 they correspond to short supermultiplets (in the sense of [6]) with quantised mass eigenvalues.…”

Section: L11mentioning

confidence: 99%

The spectrum of the S ⁵ compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4)

Günaydın

Marcus

1985

Class. Quantum Grav.

334

622

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Abstract. We calculate the spectrum of the S5 compactification of the chiral N = 2, D = 10 supergravity theory. The modes on S5 fall into unitary irreducible representations of the D = 5, N = 8 anti-de Sitter supergroup U(2,2/4). These unitary supermultiplets involve fields of spin s 2 with quantised 'mass' eigenvalues. The massless multiplet contains fifteen vector fields, six self-dual and six anti-self-dual anti-symmetric tensor fields. The fields of the massless multiplet are expected to be those of a gauged N = 8 theory in D = 5 with a local gauge group SU(4).Recently there has been a surge of interest in Kaluza-Klein type theories in the context of supergravity. The main object of study so far has been the eleven-dimensional simple supergravity of Cremmer er a1 [ 11 and various compactifications of this theory down to four dimensions have been studied. A compactification is called spontaneous if, for example, the eleven-dimensional theory admits a vacuum solution leading to a four-dimensional spacetime M4 and a seven-dimensional compact internal manifold M , parametrised by the extra seven coordinates. Then from a four-dimensional point of view the spectrum of the theory consists of massless modes and an infinite tower of massive modes at the Planck scale corresponding to the Fourier expansion on M,.In this letter we shall study the spectrum of the chiral N = 2, D = 10 supergravity theory [2] compactified on S5 down to five spacetime dimensions. This theory cannot be obtained from the eleven-dimensional supergravity by dimensional reduction in contrast to the non-chiral N = 2, D = 10 theory which can be. The non-chiral and chiral N = 2 supergravity theories can be regarded as the massless sector of type IIa and type IIb superstring theories in D = 1011. Both ofthese theories when dimensionally reduced to D = 4 give the N = 8 theory.The fields of the chiral N = 2, D = 10 supergravity are: a complex scalar cp, a complex Weyl spinor A, a complex anti-symmetric second rank tensor A,,, a complex Weyl gravitino (cIw, a real graviton ('zehnbein') e; and a real fourth-rank anti-symmetric tensor APupA. The field strength FpvpAm of the field A,,,, is self-dual in the free theory. The complex scalar field cp parametrises the non-compact coset space SU( 1, l)/U( 1)[4]. The covariant field equations of chiral N = 2, D = 10 supergravity were obtained t

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Section: L11mentioning

confidence: 99%

The spectrum of the S ⁵ compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4)

Günaydın

Marcus

1985

Class. Quantum Grav.

334

622

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“…The current interest in AdS/CFT dualities was sparked by the conjecture of Maldacena [1] relating the large N limits of certain conformal field theories in d dimensions to M-theory/string theory compactified to d+1-dimensional AdS spacetimes. Maldacena's conjecture was based on earlier work on properties of the physics of N Dp-branes in the near horizon limit [2] and the much earlier work on 10-d IIB supergravity compactified on AdS 5 × S 5 and 11-d supergravity compactified on AdS 7 × S 4 and AdS 4 × S 7 [3,4,5,6,7,8,9]. Maldacena's conjecture was formulated in a more precise manner in [10,11].…”

Section: Introductionmentioning

confidence: 99%

Erratum to: “Unitary supermultiplets of OSp(8|4) and the AdS
Günaydın
¹
,
Takemae
²

2004
Nuclear Physics B*
22
1
135
0
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We study the unitary supermultiplets of the N = 4 d = 7 anti-de Sitter (AdS 7 ) superalgebra OSp(8 * |4), with the even subalgebra SO(6, 2) × U Sp(4), which is the symmetry superalgebra of M-theory on AdS 7 × S 4 . We give a complete classification of the positive energy doubleton and massless supermultiplets of OSp(8 * |4). The ultra-short doubleton supermultiplets do not have a Poincaré limit in AdS 7 and correspond to superconformal field theories on the boundary of AdS 7 which can be identified with d = 6 Minkowski space. We show that the six dimensional Poincare mass operator m 2 = P µ P µ vanishes identically for the doubleton representations. By going from the compact U (4) basis of SO * (8) = SO(6, 2) to the noncompact basis SU * (4)×D (d = 6 Lorentz group times dilatations) one can associate the positive (conformal) energy representations of SO * (8) with conformal fields transforming covariantly under the Lorentz group in d = 6. The oscillator method used for the construction of the unitary supermultiplets of OSp(8 * |4) can be given a dynamical realization in terms of chiral super-twistor fields. CERN-TH/99-347 November, 1999 1 Work supported in part by the National Science Foundation under Grant Number PHY-9802510 2 e-mail: murat@phys.psu.edu 3 e-mail: takemae@phys.psu.edu. IntroductionRecently, a great deal of work has been done on AdS/CFT (anti-de Sitter/conformal field theory) dualities in various dimensions. The current interest in AdS/CFT dualities was sparked by the conjecture of Maldacena [1] relating the large N limits of certain conformal field theories in d dimensions to M-theory/string theory compactified to d+1-dimensional AdS spacetimes. Maldacena's conjecture was based on earlier work on properties of the physics of N Dp-branes in the near horizon limit [2] and the much earlier work on 10-d IIB supergravity compactified on AdS 5 × S 5 and 11-d supergravity compactified on AdS 7 × S 4 and AdS 4 × S 7 [3,4,5,6,7,8,9]. Maldacena's conjecture was formulated in a more precise manner in [10,11]. The relation between Maldacena's conjecture and the dynamics of the singleton and doubleton fields that live on the boundary of AdS spacetimes was reviewed in [12,13] and its relation to the spectra of maximal supergravities in eleven and ten dimensions in [13,14]. For a recent review of AdS/CFT dualities and an extensive list of references on the subject see [15].The best studied example of this AdS/CFT duality is the duality between the large N limit of the conformally invariant N = 4 SU (N ) super Yang-Mills theory in d = 4 and type IIB superstring theory on AdS 5 ×S 5 . The N = 4 Yang-Mills supermultiplet is simply the unique CPT self-conjugate doubleton supermultiplet of the symmetry superalgebra SU (2, 2|4) of type IIB superstring over AdS 5 × S 5 [4,16]. Doubleton supermultiplets do not have a smooth Poincaré limit in d = 5 and correspond to superconformal field theories on the boundary of AdS 5 , which can be identified with the four dimensional Minkowski space. The SU (2, 2|4) alg...

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“…The fact that the entire tower of Kaluza-Klein states of supergravity have integer energy levels can be interpreted in terms of the AdS supersymmetry algebra [13] (we thank Paul Townsend for pointing this out to us). They are Bogomolny-Prasad-Sommerfeld (BPS) states, forming short supersymmetry multiplets, and their levels are naturally integral.…”

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confidence: 99%

Spectrum of LargeNGauge Theory from Supergravity

Horowitz

Ooguri

1998

Phys. Rev. Lett.

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Recently, Maldacena proposed that the large N limit of the N 4 supersymmetric gauge theory in four dimensions with U͑N͒ gauge group is dual to the type IIB superstring theory on AdS 5 3 S 5 . We use this proposal to study the spectrum of the large N gauge theory on 4 3 S 3 in a low energy regime. We find that the spectrum is discrete and evenly spaced, and the number of states at each energy level is smaller than the one predicted by the naive extrapolation of the Bekenstein-Hawking formula to the low energy regime. We also show that the gauge theory describes a region of spacetime behind the horizon as well as the region in front. [S0031-9007(98) (2) because of the Bekenstein-Hawking entropy formula for the near extremal 3-brane solution of type IIB theory [3]. In general (1) can be derived by assuming that the entropy is an extensive quantity and that it is invariant under the dilatation.Recently Maldacena made an interesting proposal in [4] that compactifications of M theory and string theory on a sphere to anti-de Sitter space (AdS) are dual to various conformal field theories. In particular, the large N limit of the N 4 U͑N͒ gauge theory in four dimensions is claimed to be described by the type IIB string theory on AdS 5 3 S 5 . This implies that spectra of the two theories and, hence, the entropies are the same.The purpose of this paper is to use this proposal to learn about the spectrum of the large N gauge theory on 4 3 S 3 . We will establish a correspondence between states in this gauge theory and states in string theory on AdS 5 3 S 5 . In the supergravity approximation to string theory, the energy levels are quantized in the units of the AdS radius R ͑4pgN͒ 1͞4 l s where g is the string coupling constant, and l s is the string length,The supergravity approximation is valid, when E is less than both the string scale and the Planck scale,Since l p ϳ g 1͞4 l s in ten dimensions, we can trust the supergravity computation forIn this regime, we find that the entropy of the type IIB string theory scales as a function of E n͞R asfor n ¿ 1. We will show that each supergravity state with energy E n͞R corresponds to a state with energy E n in the gauge theory on 4 3 S 3 with a unit radius sphere. Thus, Maldacena's proposal leads to the prediction that the entropy of the large N gauge theory on 4 3 S 3 for 1 ø n ø ͑ gN͒ 1͞4 is S gauge ϳ n 9͞10 .In particular, the large N spectrum is independent of N.On the other hand, the Bekenstein-Hawking formula (2) at this energy readsSince this formula was originally derived for the 3-branes wrapped on T 3 , it is a prediction for the density of states for the gauge theory on T 3 . However, for sufficiently large n, finite size effects are irrelevant, and we expect that the density of states is independent of the topology of the 3-manifold. In such a case, we can use the formula (6) for the gauge theory on S 3 also. Comparing this with (5), the power of n is different, and there is no factor of p N in (5). Therefore, in the low energy regime (3), S gauge is smaller than the...

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Multiplet shortening in Osp(N,4)

Cited by 112 publications

References 23 publications

The spectrum of the S ⁵ compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4)

The spectrum of the S ⁵ compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4)

Erratum to: “Unitary supermultiplets of OSp(8|4) and the AdS
Günaydın
¹
,
Takemae
²

2004
Nuclear Physics B*
22
1
135
0
View full text Add to dashboard Cite

Spectrum of LargeNGauge Theory from Supergravity

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Multiplet shortening in Osp(N,4)

Cited by 112 publications

References 23 publications

The spectrum of the S 5 compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4)

The spectrum of the S 5 compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4)

Erratum to: “Unitary supermultiplets of OSp(8*|4) and the AdSGünaydın1, Takemae2 2004Nuclear Physics B2211350View full textAdd to dashboardCite

Spectrum of LargeNGauge Theory from Supergravity

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The spectrum of the S ⁵ compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4)

The spectrum of the S ⁵ compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4)

Erratum to: “Unitary supermultiplets of OSp(8|4) and the AdS
Günaydın
¹
,
Takemae
²

2004
Nuclear Physics B*
22
1
135
0
View full text Add to dashboard Cite