Supersymmetric Higher Spin Theories

We revisit the higher spin extensions of the anti de Sitter algebra in four dimensions that incorporate internal symmetries and admit representations that contain fermions, classified long ago by Konstein and Vasiliev. We construct the $dS_4$, Euclidean and Kleinian version of these algebras, as well as the corresponding fully nonlinear Vasiliev type higher spin theories, in which the reality conditions we impose on the master fields play a crucial role. The ${\cal N}=2$ supersymmetric higher spin theory in $dS_4$, on which we elaborate further, is included in this class of models. A subset of Konstein-Vasiliev algebras are the higher spin extensions of the $AdS_4$ superalgebras $osp(4|{\cal N})$ for ${\cal N}=1,2,4$ mod 4 and can be realized using fermionic oscillators. We tensor the higher superalgebras of the latter kind with appropriate internal symmetry groups and show that the ${\cal N}=3$ mod 4 higher spin algebras are isomorphic to those with ${\cal N}=4$ mod 4. We describe the fully nonlinear higher spin theories based on these algebras as well, and we elaborate further on the ${\cal N}=6$ supersymmetric theory, providing two equivalent descriptions one of which exhibits manifestly its relation to the ${\cal N}=8$ supersymmetric higher spin theory.Comment: 30 pages. Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

Modelling Quality of Service in IEEE 802.16 Networks

While only relatively recently standardized, IEEE 802.16 orWiMAX networks are receiving a great deal of attention in both industry and research. This is so because with the increased emphasis on multimedia data, apart from the general advantage of wireless, 802.16 promises wider bandwidth and QoS as part of the standard. As a back haul network for other networks, in particular the 802.11a/b/g/e or WiFi networks, it is well suited. As for any new technology, there are many open questions of which Transmission Scheduling and Connection Admission Control (CAC) are the most prominent. The standard intentionally makes no statement about either function. Different from other performance models we have seen, we consider an analytical framework which takes into account the close relationship between the CAC algorithms and the Scheduler algorithms and is applicable to each mode of operation and admission control paradigm specified by the standard. The long term objective of this work is to present a hybrid analytic and simulation model, based on the proposed framework, for modelling QoS metrics in 802.16 networks

A minimal BV action for Vasiliev's four-dimensional higher spin gravity

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle.Comment: 39 pages, 1 figure. Additional comments in the conclusion

An action principle for Vasiliev's four-dimensional higher-spin gravity

We provide Vasiliev's fully nonlinear equations of motion for bosonic gauge fields in four spacetime dimensions with an action principle. We first extend Vasiliev's original system with differential forms in degrees higher than one. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms: One set of functions that appears in the Q-structure of the generalized curvatures of the odd forms in the duality-extended system; and another set depending on the Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of polyvector fields of ranks two or higher in target space. We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal Type A and B models (with only even spins), spectral flows on-shell and provide boundary conditions on fields and gauge parameters that are compatible with the variational principle and that make the duality-extended system equivalent, on shell, to Vasiliev's original system.Comment: 37 pages. References added, corrected typo

The Higher Spin/Vector Model Duality

This paper is mainly a review of the dualities between Vasiliev's higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents. We also present some new results in the computation of parity odd structures in the three point functions in parity violating Vasiliev theories.Comment: 55 pages, 1 figure. Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev. v2: references adde

Propagating modes of non-Abelian tensor gauge field of second rank

In the recently proposed extension of the YM theory, non-Abelian tensor gauge field of the second rank is represented by a general tensor whose symmetric part describes the propagation of charged gauge boson of helicity two and its antisymmetric part - the helicity zero charged gauge boson. On the non-interacting level these polarizations are similar to the polarizations of the graviton and of the Abelian antisymmetric B field, but the interaction of these gauge bosons carrying non-commutative internal charges cannot be directly identified with the interaction of gravitons or B field. Our intention here is to illustrate this result from different perspectives which would include Bianchi identity for the corresponding field strength tensor and the analysis of the second-order partial differential equation which describes in this theory the propagation of non-Abelian tensor gauge field of the second rank.Comment: 22 pages, Latex fil

Notes on the ambient approach to boundary values of AdS gauge fields

The ambient space of dimension d+2 allows to formulate both fields on AdS(d+1) and conformal fields in d dimensions such that the symmetry algebra o(d,2) is realized linearly. We elaborate an ambient approach to the boundary analysis of gauge fields on anti de Sitter spacetime. More technically, we use its parent extension where fields are still defined on AdS or conformal space through arbitrary intrinsic coordinates while the ambient construction works in the target space. In this way, a manifestly local and o(d,2)-covariant formulation of the boundary behaviour of massless symmetric tensor gauge fields on AdS(d+1) spacetime is obtained. As a byproduct, we identify some useful ambient formulation for Fronsdal fields, conformal currents and shadow fields along with a concise generating-function formulation of the Fradkin-Tseytlin conformal fields somewhat similar to the one obtained by Metsaev. We also show how this approach extends to more general gauge theories and discuss its relation to the unfolded derivation of the boundary dynamics recently proposed by Vasiliev.Comment: Slightly expanded version of the invited contribution to the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and Mikhail Vasiliev; version 2: addition of 2 references, some comparisons with the standard AdS/CFT framework and comments on the scalar singleton cas

Black holes in three dimensional higher spin gravity: A review

We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to leading asymptotic order. In view of the AdS/CFT correspondence as applied to certain vector-like conformal field theories with extended conformal symmetry, we successfully compare to CFT calculations in a generalized Cardy regime. A brief recollection of pertinent aspects of ordinary gravity is also given.Comment: 49 pages, harvmac, invited contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

Collective Dipole Model of AdS/CFT and Higher Spin Gravity

We formulate a first quantized construction of the AdS_{d+1}/CFT_d correspondence using the bi-local representation of the free d-dimensional large N vector model. The earlier reconstruction of AdS_4 higher-spin gravity provides a scheme where the AdS spacetime (and higher-spin fields) are given by the composite bi-local fields. The underlying first quantized, world-sheet picture is extracted in the present work and generalized to any dimension. A higher-spin AdS particle model is shown to emerge from the collective bi-particle system of Minkowski particles through a canonical transformation. As such this construction provides a simple explicit mechanism of the AdS/CFT correspondence.Comment: 16 pages, no figures; v2: references added; v3: minor change