4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5

D. Minic; M. Gunaydin; M. Zagermann

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4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5

M. Gunaydin, D. Minic, M. Zagermann

High Energy Physics - Theory · Submitted 4 Jun 1998

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The authors' main claim We give a complete classification of the doubleton supermultiplets of SU(2,2|4) which do not have a Poincare limit and correspond to d=4 conformal field theories (CFT) living on the boundary of AdS_5.

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arXiv IDhep-th/9806042 (version 4)

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CitationD. Minic, M. Gunaydin, M. Zagermann. "4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5." arXiv:hep-th/9806042 (1998). https://pith.science/paper/2XSIMR7Q

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We study the unitary supermultiplets of the N=8, d=5 anti-de Sitter (AdS) superalgebra SU(2,2|4) which is the symmetry algebra of the IIB string theory on AdS_5 X S^5. We give a complete classification of the doubleton supermultiplets of SU(2,2|4) which do not have a Poincare limit and correspond to d=4 conformal field theories (CFT) living on the boundary of AdS_5. The CPT self-conjugate irreducible doubleton supermultiplet corresponds to d=4, N = 4 super Yang-Mills theory. The other irreducible doubleton supermultiplets come in CPT conjugate pairs. The maximum spin range of the general doubleton supermultiplets is 2. In particular, there exists a CPT conjugate pair of doubleton supermultiplets corresponding to the fields of N=4 conformal supergravity in d=4 which can be coupled to N=4 super Yang-Mills theory in d=4. We also study the "massless" supermultiplets of SU(2,2|4) which can be obtained by tensoring two doubleton supermultiplets. The CPT self-conjugate "massless" supermultiplet is the N=8 graviton supermultiplet in AdS_5. The other "massless" supermultiplets generally come in conjugate pairs and can have maximum spin range of 4. We discuss the implications of our results for the conjectured CFT/AdS dualities.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the unitary supermultiplets of the N=8, d=5 anti-de Sitter (AdS) superalgebra SU(2,2\|4) which is the symmetry algebra of the IIB string theory on AdS_5 X S^5.	contribution 0.68	0.75	0.04	asserted 1.00
s1	We give a complete classification of the doubleton supermultiplets of SU(2,2\|4) which do not have a Poincare limit and correspond to d=4 conformal field theories (CFT) living on the boundary of AdS_5.	contribution 0.77	0.95	0.38	asserted 1.00
s2	The CPT self-conjugate irreducible doubleton supermultiplet corresponds to d=4, N = 4 super Yang-Mills theory.	result 1.00	0.73	0.21	asserted 1.00
s3	The other irreducible doubleton supermultiplets come in CPT conjugate pairs.	result 1.00	0.81	0.08	asserted 1.00
s4	The maximum spin range of the general doubleton supermultiplets is 2.	result 1.00	0.85	0.09	asserted 1.00
s5	In particular, there exists a CPT conjugate pair of doubleton supermultiplets corresponding to the fields of N=4 conformal supergravity in d=4 which can be coupled to N=4 super Yang-Mills theory in d=4.	result 0.99	0.79	0.16	asserted 0.89
s6	We also study the "massless" supermultiplets of SU(2,2\|4) which can be obtained by tensoring two doubleton supermultiplets.	contribution 0.99	0.91	0.04	asserted 0.99
s7	The CPT self-conjugate "massless" supermultiplet is the N=8 graviton supermultiplet in AdS_5.	result 1.00	0.80	0.11	asserted 1.00
s8	The other "massless" supermultiplets generally come in conjugate pairs and can have maximum spin range of 4.	result 1.00	0.85	0.09	asserted 0.83
s9	We discuss the implications of our results for the conjectured CFT/AdS dualities.	interpretation 0.99	0.58	0.09	unclear 0.82

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We study the unitary supermultiplets of the N=8, d=5 anti-de Sitter (AdS) superalgebra SU(2,2|4) which is the symmetry algebra of the IIB string theory on AdS_5 X S^5. We give a complete classification of the doubleton supermultiplets of SU(2,2|4) which do not have a Poincare limit and correspond to d=4 conformal field theories (CFT) living on the boundary of AdS_5. The CPT self-conjugate irreducible doubleton supermultiplet corresponds to d=4, N = 4 super Yang-Mills theory. The other irreducible doubleton supermultiplets come in CPT conjugate pairs. The maximum spin range of the general doubleton supermultiplets is 2. In particular, there exists a CPT conjugate pair of doubleton supermultiplets corresponding to the fields of N=4 conformal supergravity in d=4 which can be coupled to N=4 super Yang-Mills theory in d=4. We also study the "massless" supermultiplets of SU(2,2|4) which can be obtained by tensoring two doubleton supermultiplets. The CPT self-conjugate "massless" supermultiplet is the N=8 graviton supermultiplet in AdS_5. The other "massless" supermultiplets generally come in conjugate pairs and can have maximum spin range of 4. We discuss the implications of our results for the conjectured CFT/AdS dualities.

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Cited by 6 Pith papers

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On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
hep-th 2002-09 accept novelty 6.0 of 10

At the unitarity threshold a long superconformal multiplet decomposes into four semi-short multiplets, and only the 1/2-BPS [0,p,0] and 1/4-BPS [1,p,1] multiplets are guaranteed to have protected scale dimensions.

Show 1 more citing papers

Large N Field Theories, String Theory and Gravity
hep-th 1999-05 accept novelty 3.0 of 10

The review argues and assembles the evidence that N=4 supersymmetric Yang-Mills theory in four dimensions is dual to type IIB string theory on AdS5 x S5, and surveys what the duality predicts.

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30 arXiv papers cite this in 86 sentences

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We will use the doubleton realization [ref] reviewed in section [ref] to compute the generator $J_ABCD$ of the Joseph ideal for $SO(4,2)$ : J_ABCD = M_ABM_CD - M_AB⊚M_CD - 1/2M_ABM_CD - 1/60 ⟨M_AB,M_CD ⟩ = 1/2 M_AB ·M_CD - M_AB⊚M_CD - 1/60 ⟨M_AB,M_CD ⟩Substituting the expressions for the generators in the covariant twistorial realization one finds that it does not vanish identically as an operator in contrast to the situation with the singletonic realization of $SO(3,2)$.

Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Four Dimensions · Joseph ideal in the covariant twistorial oscillator or doubleton realization · 0.89
Note that we use the same oscillator realisations of Lie algebra as in [ref] .

The complete unitary dual of non-compact Lie superalgebra su(p,q|m) via the generalised oscillator formalism, and non-compact Young diagrams · Introduction · 1.00

Compares with it 2 papers

The supermultiplet that corresponds to $ζ= -1$ (given in Table [ref]) is exactly the doubleton supermultiplet in [ref] obtained by starting from the lowest weight vector $|Ω⟩ = | , 1⟩$.

Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions · Deformed minimal unitary supermultiplets of $𝔰𝔲( 2 , 2 | 4 )$ for $ζ0$ · 0.88
Though $E$ is defined to be non-negative, in ([ref]) there is no positive $c$-number term in distinction to the case when $su(2,2)$ generators are realized solely in terms of the bosonic oscillators [ref] , [ref] .

Oscillator approach to quantization of $AdS_5\times S^5$ superparticle in twistor formulation · Oscillator realization of global $u(2,2|4)$ symmetry · 0.87

Cites it as background 14 papers

Twistorial oscillator construction of the unitary supermultiplets of $SU(2,2 | 4)$ has been studied in [ref] .

Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions · Minimal Unitary Supermultiplet of $𝔰𝔲( 2 , 2 | 4 )$ and its Deformations · 0.85
The oscillator construction of the unitary supermultiplets of extended superconformal algebras in four dimensions were first given in [ref] and further developed in [ref] .[ For classification of unitary representations of $SU(2,2|1)$ see [ref] and for $SU(2,2|N)$ for $N > 1$ see [ref] .]

Obstruction to E_{7(7)} Deformation in N=8 Supergravity · Linearized N=8 supergravity and the representations of $SU(2,2|8)$ superconformal algebra · 0.89
Higher spin theories and supersymmetric extensions in $AdS_5$ and $AdS_7$ were studied later in [ref] using the doubletonic realizations of [ref] .

Quasiconformal Group Approach to Higher Spin Algebras, their Deformations and Supersymmetric Extensions · Introduction · 0.84

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