776 research outputs found
Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups
We show that there is a remarkable connection between the harmonic superspace
(HSS) formulation of N=2, d=4 supersymmetric quaternionic Kaehler sigma models
that couple to N=2 supergravity and the minimal unitary representations of
their isometry groups. In particular, for N=2 sigma models with quaternionic
symmetric target spaces of the form G/HXSU(2) we establish a one-to-one mapping
between the Killing potentials that generate the isometry group G under Poisson
brackets in the HSS formulation and the generators of the minimal unitary
representation of G obtained by quantization of its geometric realization as a
quasiconformal group. Quasiconformal extensions of U-duality groups of four
dimensional N=2, d=4 Maxwell-Einstein supergravity theories (MESGT) had been
proposed as spectrum generating symmetry groups earlier. We discuss some of the
implications of our results, in particular, for the BPS black hole spectra of
4d, N=2 MESGTs.Comment: 20 pages; Latex file: references added; minor cosmetic change
Unitary Supermultiplets of OSp(1/32,R) and M-theory
We review the oscillator construction of the unitary representations of
noncompact groups and supergroups and study the unitary supermultiplets of
OSp(1/32,R) in relation to M-theory. OSp(1/32,R) has a singleton supermultiplet
consisting of a scalar and a spinor field. Parity invariance leads us to
consider OSp(1/32,R)_L X OSp(1/32,R)_R as the "minimal" generalized AdS
supersymmetry algebra of M-theory corresponding to the embedding of two spinor
representations of SO(10,2) in the fundamental representation of Sp(32,R). The
contraction to the Poincare superalgebra with central charges proceeds via a
diagonal subsupergroup OSp(1/32,R)_{L-R} which contains the common subgroup
SO(10,1) of the two SO(10,2) factors. The parity invariant singleton
supermultiplet of OSp(1/32,R)_L \times OSp(1/32,R)_R decomposes into an
infinite set of "doubleton" supermultiplets of the diagonal
OSp(1/32,R)_{L-R}. There is a unique "CPT self-conjugate" doubleton
supermultiplet whose tensor product with itself yields the "massless"
generalized AdS_{11} supermultiplets. The massless graviton supermultiplet
contains fields corresponding to those of 11-dimensional supergravity plus
additional ones. Assuming that an AdS phase of M-theory exists we argue that
the doubleton field theory must be the holographic superconformal field theory
in ten dimensions that is dual to M-theory in the same sense as the duality
between the N=4 super Yang-Mills in d=4 and the IIB superstring over AdS_5 X
S^5.Comment: 25 pages, LaTex ; footnotes 5 and 6 modified and 3 new references
adde
Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
After reviewing the algebraic structures that underlie the geometries of N=2
Maxwell-Einstein supergravity theories (MESGT) in five and four dimensions with
symmetric scalar manifolds, we give a unified realization of their three
dimensional U-duality groups as spectrum generating quasiconformal groups. They
are F_{4(4)}, E_{6(2)}, E_{7(-5)}, E_{8(-24)} and SO(n+2,4). Our formulation is
covariant with respect to U-duality symmetry groups of corresponding five
dimensional supergravity theories, which are SL(3,R), SL(3,C), SU*(6), E_{6(6)}
and SO(n-1,1)X SO(1,1), respectively. We determine the spherical vectors of
quasiconformal realizations of all these groups twisted by a unitary character.
We also give their quadratic Casimir operators and determine their values. Our
work lays the algebraic groundwork for constructing the unitary representations
of these groups induced by their geometric quasiconformal actions, which
include the quaternionic discrete series. For rank 2 cases, SU(2,1) and
G_{2(2)}, corresponding to simple N=2 supergravity in four and five dimensions,
this program was carried out in arXiv:0707.1669. We also discuss the
corresponding algebraic structures underlying symmetries of matter coupled N=4
and N>4 supergravity theories. They lead to quasiconformal realizations of
split real forms of U-duality groups as a straightforward extension of the
quaternionic real forms.Comment: Section 4 is split with the addition of a subsection on quadratic
Casimir operators; references added; typos corrected. Latex file; 53 page
Gauging the Full R-Symmetry Group in Five-dimensional, N=2 Yang-Mills/Einstein/tensor Supergravity
We show that certain five dimensional, N=2 Yang-Mills/Einstein supergravity
theories admit the gauging of the full R-symmetry group, SU(2)_R, of the
underlying N=2 Poincare superalgebra. This generalizes the previously studied
Abelian gaugings of U(1)_R subgroup of SU(2)_R and completes the construction
of the most general vector and tensor field coupled five dimensional N=2
supergravity theories with gauge interactions. The gauging of SU(2)_R turns out
to be possible only in special cases, and leads to a new type of scalar
potential. For a large class of these theories the potential does not have any
critical points.Comment: Latex file, 15 pages ; section two is split in two and the discussion
of the critical points is moved into the new section. Version to appear in
Physical Review
The Gauging of Five-dimensional, N=2 Maxwell-Einstein Supergravity Theories coupled to Tensor Multiplets
We study the general gaugings of N=2 Maxwell-Einstein supergravity theories
(MESGT) in five dimensions, extending and generalizing previous work. The
global symmetries of these theories are of the form SU(2)_R X G, where SU(2)_R
is the R-symmetry group of the N=2 Poincare superalgebra and G is the group of
isometries of the scalar manifold that extend to symmetries of the full action.
We first gauge a subgroup K of G by turning some of the vector fields into
gauge fields of K while dualizing the remaining vector fields into tensor
fields transforming in a non-trivial representation of K. Surprisingly, we find
that the presence of tensor fields transforming non-trivially under the
Yang-Mills gauge group leads to the introduction of a potential which does not
admit an AdS ground state. Next we give the simultaneous gauging of the U(1)_R
subgroup of SU(2)_R and a subgroup K of G in the presence of K-charged tensor
multiplets. The potential introduced by the simultaneous gauging is the sum of
the potentials introduced by gauging K and U(1)_R separately. We present a list
of possible gauge groups K and the corresponding representations of tensor
fields. For the exceptional supergravity we find that one can gauge the SO^*(6)
subgroup of the isometry group E_{6(-26)} of the scalar manifold if one
dualizes 12 of the vector fields to tensor fields just as in the gauged N=8
supergravity.Comment: Latex file, 23 page
Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups
We study the symmetries of generalized spacetimes and corresponding phase
spaces defined by Jordan algebras of degree three. The generic Jordan family of
formally real Jordan algebras of degree three describe extensions of the
Minkowskian spacetimes by an extra "dilatonic" coordinate, whose rotation,
Lorentz and conformal groups are SO(d-1), SO(d-1,1) XSO(1,1) and
SO(d,2)XSO(2,1), respectively. The generalized spacetimes described by simple
Jordan algebras of degree three correspond to extensions of Minkowskian
spacetimes in the critical dimensions (d=3,4,6,10) by a dilatonic and extra
(2,4,8,16) commuting spinorial coordinates, respectively. The Freudenthal
triple systems defined over these Jordan algebras describe conformally
covariant phase spaces. Following hep-th/0008063, we give a unified geometric
realization of the quasiconformal groups that act on their conformal phase
spaces extended by an extra "cocycle" coordinate. For the generic Jordan family
the quasiconformal groups are SO(d+2,4), whose minimal unitary realizations are
given. The minimal unitary representations of the quasiconformal groups F_4(4),
E_6(2), E_7(-5) and E_8(-24) of the simple Jordan family were given in our
earlier work hep-th/0409272.Comment: A typo in equation (37) corrected and missing titles of some
references added. Version to be published in JHEP. 38 pages, latex fil
4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5
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.Comment: An erratum attached at the end to correct an incorrect statement in
section 7; 34 pages, Latex fil
Lectures on Spectrum Generating Symmetries and U-duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace
We review the underlying algebraic structures of supergravity theories with
symmetric scalar manifolds in five and four dimensions, orbits of their
extremal black hole solutions and the spectrum generating extensions of their
U-duality groups. For 5D, N=2 Maxwell-Einstein supergravity theories (MESGT)
defined by Euclidean Jordan algebras, J, the spectrum generating symmetry
groups are the conformal groups Conf(J) of J which are isomorphic to their
U-duality groups in four dimensions. Similarly, the spectrum generating
symmetry groups of 4D, N=2 MESGTs are the quasiconformal groups QConf(J)
associated with J that are isomorphic to their U-duality groups in three
dimensions. We then review the work on spectrum generating symmetries of
spherically symmetric stationary 4D BPS black holes, based on the equivalence
of their attractor equations and the equations for geodesic motion of a
fiducial particle on the target spaces of corresponding 3D supergravity
theories obtained by timelike reduction. We also discuss the connection between
harmonic superspace formulation of 4D, N=2 sigma models coupled to supergravity
and the minimal unitary representations of their isometry groups obtained by
quantizing their quasiconformal realizations. We discuss the relevance of this
connection to spectrum generating symmetries and conclude with a brief summary
of more recent results.Comment: 55 pages; Latex fil
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 authors calculate the spectrum of the S^5 compactification of the chiral N=2, D=10 supergravity theory. The modes on S^5 fall into unitary irreducible representations of the D=5, N=8 anti-de Sitter supergroup U(2,2/4). These unitary supermultiplets involve field of spin <or=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)
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