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 Gauge Theories in Various Dimensions

Properties of nonlinear higher spin gauge theories of totally symmetric massless higher spin fields in anti-de Sitter space of any dimension are discussed with the emphasize on the general aspects of the approach.Comment: LaTeX, 20 pages, Unified version of the talks delivered at International Workshop "Supersymmetries and Quantum Symmetries" (SQS'03, Dubna, Russia, July 24-29, 2003), 27th Johns Hopkins Workshop (Goteborg, Sweden, August 24-26) and 36th International Symposium Ahrenshoop on the Theory of Elementary Particles (Berlin, Germany, 26-30 Aug 2003); typos corrected, reference adde

On the Local Frame in Nonlinear Higher-Spin Equations

Properties of the resolution operator ${\rm d}_{loc}^*$ in higher-spin equations, that leads to local current interactions at the cubic order and minimally nonlocal higher-order corrections, are formulated in terms of the condition on the class of master fields of higher-spin theory that restricts both the dependence on the spinor $Y$, $Z$ variables and on the contractions of indices between the constituent fields in bilinear terms. The Green function in the sector of zero-forms is found for the case of constituent fields carrying helicities of opposite signs. It is shown that the local resolution ${\rm d}_{loc}^*$ differs from the conventional De Rham resolution ${\rm d}_Z^*$ by a non-local shift.Comment: 26 pages; V2: typos corrected, version published in JHE