Novel supermultiplets of SU(2,2|4) and the AdS_5/CFT_4 duality

We continue our study of the unitary supermultiplets of the N=8, d=5 anti-de Sitter (AdS_5) superalgebra SU(2,2|4), which is also the N=4 extended conformal superalgebra in d=4. We show explicitly how to go from the compact SU(2)XSU(2)XU(1) basis to the non-compact SL(2,C)XD basis of the positive energy unitary representations of the conformal group SU(2,2) in d=4. The doubleton representations of the AdS_5 group SU(2,2), which do not have a smooth Poincare limit in d=5, are shown to represent fields with vanishing masses in four dimensional Minkowski space. The unique CPT self-conjugate irreducible doubleton supermultiplet of SU(2,2|4)is simply the N=4 Yang-Mills supermultiplet in d=4. We study some novel short non-doubleton supermultiplets of SU(2,2|4) that have spin range 2 and that do not appear in the Kaluza-Klein spectrum of type IIB supergravity or in tensor products of the N=4 Yang-Mills supermultiplet with itself. These novel supermultiplets can be obtained from tensoring chiral doubleton supermultiplets, some of which we expect to be related to the massless limits of 1/4 BPS states. Hence, these novel supermultiplets may be relevant to the solitonic sector of IIB superstring and/or (p,q) superstrings over AdS_5 X S^5.Comment: Minor modifications to clarify the role of central charge and the outer automorphism group U(1)_Y in the representation theory of SU(2,2|4); typos corrected; 28 pages; Late

N=1,2 4D Superconformal Field Theories and Supergravity in AdS5AdS_5

We consider D3 branes world-volume theories substaining $N=1,2$ superconformal field theories. Under the assumption that these theories are dual to $N=2,4$ supergravities in $AdS_5$, we explore the general structure of the latter and discuss some issues when comparing the bulk theory to the boundary singleton theory.Comment: 12 pages, harvmac, typos correcte

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

We review the current status of the construction of unitary representations of U-duality groups of supergravity theories in five, four and three dimensions. We focus mainly on the maximal supergravity theories and on the N=2 Maxwell-Einstein 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 U-duality groups in three dimensions. 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.Comment: 24 pages; latex fil

Realizations of exceptional U-duality groups as conformal and quasiconformal groups and their minimal unitary representations

We review the novel quasiconformal realizations of exceptional U-duality groups whose "quantization" lead directly to their minimal unitary irreducible representations. 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 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. These conformal and quasiconformal groups act as spectrum generating symmetry groups in five and four dimensions and are isomorphic to the U-duality groups of the corresponding supergravity theories in four and three dimensions, respectively. Hence the spectra of these theories are expected to form unitary representations of these groups whose minimal unitary realizations are also reviewed.Comment: Invited talk at the first Gunnar Nordstroem Symposium on Theoretical Physics (Helsinki, Aug. 2003

Generalized AdS/CFT Dualities and Space-Time Symmetries of M/Superstring Theory

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).Comment: Latex file, 11 pages; invited talk to appear in the Proceedings of the IXth Marcel Grossmann Meeting (Rome, July 2000

Generalized Conformal and Superconformal Group Actions and Jordan Algebras

We study the conformal groups of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where "p-angles" can be defined. We give an oscillator realization of the generalized conformal groups of Jordan algebras and Jordan triple systems(JTS). These results are extended to Jordan superalgebras and super JTS's. We give the conformal algebras of simple Jordan algebras, hermitian JTS's and the simple Jordan superalgebras as classified by Kac.Comment: 13 pp, IASSNS-HEP-92/8

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

The quasiconformal method provides us with a unified approach to the construction of minimal unitary representations (minrep) of noncompact groups, their deformations as well as their supersymmetric extensions. We review the quasiconformal construction of the minrep of SO(d,2), its deformations and their applications to unitary realizations of AdS_{(d+1)}/CFT_d higher spin algebras and their deformations for arbitrary d and supersymmetric extensions for dimensions d less than seven. AdS_{(d+1)}/CFT_d higher spin algebras, their deformations and supersymmetric extensions are given by the enveloping algebras of the quasiconformal realizations of the minrep, its deformations and supersymmetric extensions, respectively, and are in one-to-one correspondence with massless conformal fields for arbitrary d and massless conformal supermultiplets for dimensions d less than seven.Comment: 36 pages; latex file; To appear in the "Proceedings of the International Workshop on Higher Spin Gauge Theories" , Singapore, November 4-6, 201

On the Chiral Rings in N=2 and N=4 Superconformal Algebras

We study the chiral rings in N=2 and N=4 superconformal algebras. The chiral primary states of N=2 superconformal algebras realized over hermitian triple systems are given. Their coset spaces G/H are hermitian symmetric which can be compact or non-compact. In the non-compact case, under the requirement of unitarity of the representations of G we find an infinite set of chiral primary states associated with the holomorphic discrete series representations of G. Further requirement of the unitarity of the corresponding N=2 module truncates this infinite set to a finite subset. The chiral primary states of the N=2 superconformal algebras realized over Freudenthal triple systems are also studied. These algebras have the special property that they admit an extension to N=4 superconformal algebras with the gauge group SU(2)XSU(2)XU(1). We generalize the concept of the chiral rings to N=4 superconformal algebras. We find four different rings associated with each sector (left or right moving). We also show that our analysis yields all the possible rings of N=4 superconformal algebras.Comment: 29 Page

Minimal unitary representation of SO*(8) = SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions

We study the minimal unitary representation (minrep) of SO(6,2) over an Hilbert space of functions of five variables, obtained by quantizing its quasiconformal realization. The minrep of SO(6,2), which coincides with the minrep of SO*(8) similarly constructed, corresponds to a massless conformal scalar field in six spacetime dimensions. There exists a family of "deformations" of the minrep of SO*(8) labeled by the spin t of an SU(2)_T subgroup of the little group SO(4) of lightlike vectors. These deformations labeled by t are positive energy unitary irreducible representations of SO*(8) that describe massless conformal fields in six dimensions. The SU(2)_T spin t is the six dimensional counterpart of U(1) deformations of the minrep of 4D conformal group SU(2,2) labeled by helicity. We also construct the supersymmetric extensions of the minimal unitary representation of SO*(8) to minimal unitary representations of OSp(8*|2N) that describe massless six dimensional conformal supermultiplets. The minimal unitary supermultiplet of OSp(8*|4) is the massless supermultiplet of (2,0) conformal field theory that is believed to be dual to M-theory on AdS_7 x S^4.Comment: Revised with modified notation; Typos corrected; 58 pages; Latex fil