392 research outputs found

    Gauge Fields and Singletons of AdS2p+1AdS_{2p+1}

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    We show that pp-forms on AdS2p+1AdS_{2p+1} describe both singletons and massless particles. On the 2p2p-dimensional boundary the singleton pp-form Lagrangian reduces to the conformally invariant functional ∫F2\int F^2. 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 AdS5_5 and AdS7_7 supergravity respectively.Comment: tex file, 13 page

    The Ideals of Free Differential Algebras

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    We consider the free C{\bf C}-algebra Bq{\cal B}_q with NN generators {Οi}i=1,...,N\{\xi_i\}_{i = 1,...,N}, together with a set of NN differential operators {∂i}i=1,...,N\{\partial_i\}_{i = 1,...,N} that act as twisted derivations on Bq{\cal B}_q according to the rule ∂iΟj=ÎŽij+qijΟj∂i\partial_i\xi_j = \delta_{ij} + q_{ij}\xi_j\partial_i; that is, ∀x∈Bq,∂i(Οjx)=ÎŽijx+qijΟj∂ix,\forall x \in {\cal B}_q, \partial_i(\xi_jx) = \delta_{ij}x + q_{ij}\xi_j\partial_i x, and ∂iC=0\partial_i{\bf C} = 0. The suffix qq on Bq{\cal B}_q stands for {qij}i,j∈{1,...,N}\{q_{ij}\}_{i,j \in \{1,...,N\}} and is interpreted as a point in parameter space, q={qij}∈CN2q = \{q_{ij}\}\in {\bf C}^{N^2}. A constant C∈BqC \in {\cal B}_q is a nontrivial element with the property ∂iC=0,i=1,...,N\partial_iC = 0, i = 1,...,N. To each point in parameter space there correponds a unique set of constants and a differential complex. There are no constants when the parameters qijq_{ij} are in general position. We obtain some precise results concerning the algebraic surfaces in parameter space on which constants exist. Let Iq{\cal I}_q denote the ideal generated by the constants. We relate the quotient algebras Bqâ€Č=Bq/Iq{\cal B}_q' = {\cal B}_q/{\cal I}_q 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 qq-differential equations are related to Hochschild cohomology. It is shown that Hp(Bqâ€Č,Bqâ€Č)=0H^p({\cal B}_q',{\cal B}_q') = 0 for p≄1p \geq 1. 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

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    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

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    The recent high-precision data for the reaction Îłp→pηâ€Č\gamma p\to p\eta' 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 ηâ€Č\eta' photoproduction can be described quite well over the entire energy range of available data by considering S11S_{11}, P11P_{11}, P13P_{13}, and D13D_{13} resonances, in addition to the tt-channel mesonic currents. The observed angular distribution is due to the interference between the tt-channel and the nucleon ss- and uu-channel resonance contributions. The j=3/2j=3/2 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 NNηâ€ČNN\eta^\prime 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

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    We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras so(2,d)so(2,d). We classify gauge theories invariant under so(2,d)so(2,d), both integral and half-integral spins. A similar analysis is carried out for the algebras so∗(2n)so^*(2n). We study new unitary modules of the conformal algebra in d>4d>4, that have no analogue for d≀4d\leq 4 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" pp-branes of which tensionless strings in d=6d=6 are just particular examples.Comment: 26 pages, few comments added, new references included, typos correcte

    Massless Particles in Arbitrary Dimensions

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    Various properties of two kinds of massless representations of the n-conformal (or (n+1)-De Sitter) group G~n=SO~0(2,n)\tilde{G}_n=\widetilde{SO}_0(2,n) are investigated for n≄2n\ge2. It is found that, for space-time dimensions n≄3n\ge3, the situation is quite similar to the one of the n=4 case for SnS_n-massless representations of the n-De Sitter group SO~0(2,n−1)\widetilde{SO}_0(2,n-1). These representations are the restrictions of the singletons of G~n\tilde{G}_n. 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 n≄3n\ge3.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

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    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 AdSd+1AdS_{d+1}

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    We use the correspondence between scalar field theory on AdSd+1AdS_{d+1} and a conformal field theory on RdR^d 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

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    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 Y(s1,...,sk)Y(s_1,...,s_k) with kk rows. The procedure is based on the construction of Verma modules and finding auxiliary oscillator realizations for the symplectic sp(2k)sp(2k) 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

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    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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