On Sp(2M) Invariant Green Functions

Explicit form of two-point and three-point Sp(2M) invariant Green functions is found.Comment: 7 page

Star-Product and Massless Free Field Dynamics in AdS4AdS_4

Generic solution of free equations for massless fields of an arbitrary spin in $AdS_4$ is built in terms of the star-product algebra with spinor generating elements. A class of "plane wave" solutions is described explicitly.Comment: 12 pages, latex, no figures. v4: erroneous typos in Eqs. (3.3), (3.6), (3.7) correcte

Nonlinear Equations for Symmetric Massless Higher Spin Fields in (A)dSd(A)dS_d

Nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented.Comment: 19 pages, latex, no figures, v2 minor correction

Currents of Arbitrary Spin in AdS3AdS_3

We study conserved currents of any integer or half integer spin built from massless scalar and spinor fields in $AdS_3$. 2-forms dual to the conserved currents in $AdS_3$ are shown to be exact in the class of infinite expansions in higher derivatives of the matter fields with the coefficients containing inverse powers of the cosmological constant. This property has no analog in the flat space and may be related to the holography of the AdS spaces.Comment: LaTeX, 11 pages, no figures; minor changes, version to appear in Phys.Lett.

Free Field Dynamics in the Generalized AdS (Super)Space

Pure gauge representation for general vacuum background fields (Cartan forms) in the generalized $AdS$ superspace identified with $OSp(L,M)$ is found. This allows us to formulate dynamics of free massless fields in the generalized $AdS$ space-time and to find their (generalized) conformal and higher spin field transformation laws. Generic solution of the field equations is also constructed explicitly. The results are obtained with the aid of the star product realization of ortosymplectic superalgebras.Comment: Some notes added, corrected typo

Higher-Spin Matter Interactions in 2+1 Dimensions

We describe a model of massive matter fields interacting through higher-spin gauge fields in 2+1 dimensional space-time. The two main conclusions are that the parameter of mass $M$ appears as a module characterizing an appropriate vacuum solution of the full non-linear model and that $M$ affects a structure of a global vacuum higher-spin symmetry which leaves invariant the chosen vacuum solution.Comment: LaTex, 9 pages, no figures, Invited talk at the 10 International Conference Problems of Quantum Field Theory, Alushta (Cremea - Ukrain), May 13-18, 199

Static BPS black hole in 4d higher-spin gauge theory

We find exact spherically symmetric solution of 4d nonlinear bosonic higher-spin gauge theory, that preserves a quarter of supersymmetries of N=2 supersymmetric 4d higher-spin gauge theory. In the weak field regime it describes $AdS_4$ Schwarzschild black hole in the spin two sector along with non-zero massless fields of all integer spins.Comment: 16 pages, no figures, A section with the analysis of global symmetries is added. It is shown that the obtained solution is static and supersymmetric. The title is changed correspondingly. Clarifications and references added. Typos related to reality conditions fixe

Coordinate-Free Action for AdS3 Higher-Spin-Matter Systems

A coordinate-free action principle for the N=2 supersymmetric model of spin 0 and spin 1/2 matter fields interacting via Chern-Simons higher spin gauge fields in AdS3 is formulated in terms of star-product algebra of two oscillators. Although describing proper relativistic dynamics the action does not contain space-time coordinates. It is given by a supertrace of a forth-order polynomial in the 3d higher spin superalgebra. The theory admits a free parameter characterizing the inequivalent vacua associated with the parameter of mass m of the matter fields. For the case of the massless matter, the model has a form of the noncommutative 2d Yang-Mills theory with some infinite-dimensional gauge group. The limit m\to\infty corresponds to the SU(\infty) 2d Yang-Mills theory.Comment: LaTeX, 14 pages, no figures; revised version to be published in Phys.Lett.

Superspace Formulation of 4D Higher Spin Gauge Theory

Interacting AdS_4 higher spin gauge theories with N \geq 1 supersymmetry so far have been formulated as constrained systems of differential forms living in a twistor extension of 4D spacetime. Here we formulate the minimal N=1 theory in superspace, leaving the internal twistor space intact. Remarkably, the superspace constraints have the same form as those defining the theory in ordinary spacetime. This construction generalizes straightforwardly to higher spin gauge theories N>1 supersymmetry.Comment: 24 p

Higher Spin Gauge Theories in Any Dimension

Some general properties of higher spin gauge theories are summarized with the emphasize on the nonlinear theories in any dimension.Comment: 15 pages, Proceedings of Strings 2004, Paris, June 28-July