1,981 research outputs found

### 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 $AdS_5$

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

### 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

### 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

### 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

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