Direct construction of a cubic selfinteraction for higher spin gauge fields

Using Noether's procedure we directly construct a complete cubic selfinteraction for the case of spin s=4 in a flat background and discuss the cubic selfinteraction for general spin s with s derivatives in the same background. The leading term of the latter interaction together with the leading gauge transformation of first field order are presented.Comment: Latex, 20 pages, v.2 minor changes, references added, v.3 accepted in Nucl.Phys.

On Nonlinear Higher Spin Curvature

We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider in detail the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the deWit-Freedman curvature.Comment: 12 page

The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of AdS4AdS_{4}

An analysis of the structure and singularities of the one loop two point function of the higher spin traceless and conserved currents constructed from the single scalar field in $AdS$ space is presented. The detailed renormalization procedure is constructed and the quantum violation of the traceless Ward identity is investigated. The connection with the one loop effective action for higher spin gauge fields is discussed.Comment: 23 pages, Latex, misprints corrected, v.3 two sections added, v.4 published version in Nucl. Phys.

A generating function for the cubic interactions of higher spin fields

We present an off-shell generating function for all cubic interactions of Higher Spin gauge fields constructed in arXiv:1003.2877. It is a generalization of the on-shell generating function proposed in arXiv:1006.5242, is written in a very compact way, and turns out to have a remarkable structure.Comment: 14 pages, Latex,v.2 misprints corrected, v.3 ref. added, v. 4 published in Phys. Lett.

The structure of the trace anomaly of higher spin conformal currents in the bulk of AdS4AdS_{4}

The two-point function of the conserved traceless spin-$\ell$ currents which are constructed from the scalar field $\sigma(z)$ is evaluated and renormalized by a dimensional regularization procedure. The anomaly is managed to arise only in the trace part. To isolate this trace anomaly it is sufficient to analyze only the maximum singular part of the two-point function and its trace terms to leading order. The corresponding part of the effective action which is quadratic in the trace of the higher spin field is explicitly given. For the spin-2 field which is identical with the gravitational field the results known from the literature are reproduced.Comment: latex, 21 pages,v.2 minor addition, ref. added, v.3 accepted in Nucl.Phys.

Conformal invariant interaction of a scalar field with the higher spin field in AdS_{D}

The explicit form of linearized gauge invariant interactions of scalar and general higher even spin fields in the $AdS_{D}$ space is obtained. In the case of general spin $\ell$ a generalized 'Weyl' transformation is proposed and the corresponding 'Weyl' invariant action is constructed. In both cases the invariant actions of the interacting higher even spin gauge field and the scalar field include the whole tower of invariant actions for couplings of the same scalar with all gauge fields of smaller even spin. For the particular value of $\ell=4$ all results are in exact agreement with hep-th/0403241Comment: 18 pages, Latex,v.2 accepted in Mod. Phys. Lett.