392 research outputs found
Gauge Fields and Singletons of
We show that -forms on describe both singletons and massless
particles. On the -dimensional boundary the singleton -form Lagrangian
reduces to the conformally invariant functional . All the
representations, singletons as well as massless, are zero center modules and
involve a vacuum mode. Two- and three-form singleton fields are required by
supersymmetry in AdS and AdS supergravity respectively.Comment: tex file, 13 page
The Ideals of Free Differential Algebras
We consider the free -algebra with generators
, together with a set of differential operators
that act as twisted derivations on
according to the rule ;
that is, and . The suffix on stands for and is interpreted as a
point in parameter space, . A constant is a nontrivial element with the property . To each point in parameter space there correponds a unique set of
constants and a differential complex. There are no constants when the
parameters are in general position. We obtain some precise results
concerning the algebraic surfaces in parameter space on which constants exist.
Let denote the ideal generated by the constants. We relate the
quotient algebras to Yang-Baxter algebras
and, in particular, to quantized Kac-Moody algebras. The differential complex
is a generalization of that of a quantized Kac-Moody algebra described in terms
of Serre generators. Integrability conditions for -differential equations
are related to Hochschild cohomology. It is shown that for . The intimate relationship to generalized, quantized
Kac-Moody algebras suggests an approach to the problem of classification of
these algebras.Comment: 31 pages. Plain TeX. Typos corrected, minor changes done and section
3.5.6 partially rewritten. To appear in Journal of Algebr
On Tensorial Spaces and BCFW Recursion Relations for Higher Spin Fields
In this short review we briefly consider two topics in the higher spin gauge
theory: the method of "tensorial (super) spaces" and application of BCFW
recursion relations to higher spin fields.Comment: 26 pages, Invited Review, discussion improved, references adde
Analyzing eta' photoproduction data on the proton at energies of 1.5--2.3 GeV
The recent high-precision data for the reaction at
photon energies in the range 1.5--2.3 GeV obtained by the CLAS collaboration at
the Jefferson Laboratory have been analyzed within an extended version of the
photoproduction model developed previously by the authors based on a
relativistic meson-exchange model of hadronic interactions [Phys. Rev. C
\textbf{69}, 065212 (2004)]. The photoproduction can be described quite
well over the entire energy range of available data by considering ,
, , and resonances, in addition to the -channel
mesonic currents. The observed angular distribution is due to the interference
between the -channel and the nucleon - and -channel resonance
contributions. The resonances are required to reproduce some of the
details of the measured angular distribution. For the resonances considered,
our analysis yields mass values compatible with those advocated by the Particle
Data Group. We emphasize, however, that cross-section data alone are unable to
pin down the resonance parameters and it is shown that the beam and/or target
asymmetries impose more stringent constraints on these parameter values. It is
found that the nucleonic current is relatively small and that the
coupling constant is not expected to be much larger than 2.Comment: Revised version based on revised (finalized) CLAS data (14 pages, 10
figures, RevTeX4
Conformal Fields in Higher Dimensions
We generalize, to any space-time dimension, the unitarity bounds of highest
weight UIR's of the conformal groups with Lie algebras . We classify
gauge theories invariant under , both integral and half-integral
spins. A similar analysis is carried out for the algebras . We study
new unitary modules of the conformal algebra in , that have no analogue
for as they cannot be obtained by "squaring" singletons. This may
suggest the interpretation of higher dimensional non-trivial conformal field
theories as theories of "tensionless" -branes of which tensionless strings
in are just particular examples.Comment: 26 pages, few comments added, new references included, typos
correcte
Massless Particles in Arbitrary Dimensions
Various properties of two kinds of massless representations of the
n-conformal (or (n+1)-De Sitter) group are
investigated for . It is found that, for space-time dimensions ,
the situation is quite similar to the one of the n=4 case for -massless
representations of the n-De Sitter group . These
representations are the restrictions of the singletons of . The
main difference is that they are not contained in the tensor product of two
UIRs with the same sign of energy when n>4, whereas it is the case for another
kind of massless representation. Finally some examples of Gupta-Bleuler
triplets are given for arbitrary spin and .Comment: 33 pages, LaTeX2e. To be published in Reviews in Math. Phy
Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties
If a state is passive for uniformly accelerated observers in n-dimensional
anti-de Sitter space-time (i.e. cannot be used by them to operate a perpetuum
mobile), they will (a) register a universal value of the Unruh temperature, (b)
discover a PCT symmetry, and (c) find that observables in complementary
wedge-shaped regions necessarily commute with each other in this state. The
stability properties of such a passive state induce a "geodesic causal
structure" on AdS and concommitant locality relations. It is shown that
observables in these complementary wedge-shaped regions fulfill strong
additional independence conditions. In two-dimensional AdS these even suffice
to enable the derivation of a nontrivial, local, covariant net indexed by
bounded spacetime regions. All these results are model-independent and hold in
any theory which is compatible with a weak notion of space-time localization.
Examples are provided of models satisfying the hypotheses of these theorems.Comment: 27 pages, 1 figure: dedicated to Jacques Bros on the occasion of his
70th birthday. Revised version: typos corrected; as to appear in J. Math.
Phy
Conformal Field Theory Correlators from Classical Scalar Field Theory on
We use the correspondence between scalar field theory on and a
conformal field theory on to calculate the 3- and 4-point functions of
the latter. The classical scalar field theory action is evaluated at tree
level.Comment: 9 pages, LaTeX2e with amsmath, amsfonts packages, section 2
rewritten, references adde
On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds
We review the details of unconstrained Lagrangian formulations for Bose
particles propagated on an arbitrary dimensional flat space-time and described
by the unitary irreducible integer higher-spin representations of the Poincare
group subject to Young tableaux with rows. The procedure
is based on the construction of Verma modules and finding auxiliary oscillator
realizations for the symplectic algebra which encodes the second-class
operator constraints subsystem in the HS symmetry algebra. Application of an
universal BRST approach reproduces gauge-invariant Lagrangians with reducible
gauge symmetries describing the free dynamics of both massless and massive
bosonic fields of any spin with appropriate number of auxiliary fields.Comment: 8 pages, no figures, extended Contribution to the Proceedings of the
International Workshop "Supersymmetry and Quantum Symmetries" (SQS'2011, July
18- July 23, 2011, Dubna, Russia), v.2: 9 pages, 2 references with comments
in Introduction adde
Extrinsic Curvature Embedding Diagrams
Embedding diagrams have been used extensively to visualize the properties of
curved space in Relativity. We introduce a new kind of embedding diagram based
on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an
extrinsic curvature embedding diagram, when used together with the usual kind
of intrinsic curvature embedding diagram, carries the information of how a
surface is {\it embedded} in the higher dimensional curved space. Simple
examples are given to illustrate the idea.Comment: 22 pages, 4 figure
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