90 research outputs found
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
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
Massless conformal fields, AdS_{d+1}/CFT_d higher spin algebras and their deformations
We extend our earlier work on the minimal unitary representation of
and its deformations for and to arbitrary dimensions . We show
that there is a one-to-one correspondence between the minrep of and
its deformations and massless conformal fields in Minkowskian spacetimes in
dimensions. The minrep describes a massless conformal scalar field, and its
deformations describe massless conformal fields of higher spin. The generators
of Joseph ideal vanish identically as operators for the quasiconformal
realization of the minrep, and its enveloping algebra yields directly the
standard bosonic higher spin algebra. For deformed minreps
the generators of certain deformations of Joseph ideal vanish as operators and
their enveloping algebras lead to deformations of the standard bosonic higher
spin algebra. In odd dimensions there is a unique deformation of the higher
spin algebra corresponding to the spinor singleton. In even dimensions one
finds infinitely many deformations of the higher spin algebra labelled by the
eigenvalues of Casimir operator of the little group for massless
representations.Comment: 41 pages; LaTeX file; Minor improvements in presentation; Typos
corrected; References added; Version published in NP
Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six Dimensions
Massless conformal scalar field in six dimensions corresponds to the minimal
unitary representation (minrep) of the conformal group SO(6,2). This minrep
admits a family of deformations labelled by the spin t of an SU(2)_T group,
which is the 6d analog of helicity in four dimensions. These deformations of
the minrep of SO(6,2) describe massless conformal fields that are symmetric
tensors in the spinorial representation of the 6d Lorentz group. The minrep and
its deformations were obtained by quantization of the nonlinear realization of
SO(6,2) as a quasiconformal group in arXiv:1005.3580. We give a novel
reformulation of the generators of SO(6,2) for these representations as
bilinears of deformed twistorial oscillators which transform nonlinearly under
the Lorentz group SO(5,1) and apply them to define higher spin algebras and
superalgebras in AdS_7. The higher spin (HS) algebra of Fradkin-Vasiliev type
in AdS_7 is simply the enveloping algebra of SO(6,2) quotiented by a two-sided
ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph
ideal vanishes identically for the quasiconformal realization of the minrep and
its enveloping algebra leads directly to the HS algebra in AdS_7. Furthermore,
the enveloping algebras of the deformations of the minrep define a discrete
infinite family of HS algebras in AdS_7 for which certain 6d Lorentz covariant
deformations of the Joseph ideal vanish identically. These results extend to
superconformal algebras OSp(8*|2N) and we find a discrete infinite family of HS
superalgebras as enveloping algebras of the minimal unitary supermultiplet and
its deformations. Our results suggest the existence of a discrete family of
(supersymmetric) HS theories in AdS_7 which are dual to free (super)conformal
field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in
6d.Comment: 30 pages; Latex file; Discussion in section 3.2 expanded; typos
corrected; minor modifications; version to be published in JHE
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