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.

Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in d=4d=4

We construct all possible Weyl invariant actions in $d=4$ for linearized spin three field in a general gravitational background. The first action is obtained as the square of the generalized Weyl tensor for a spin three gauge field in nonlinear gravitational background. It is, however, not invariant under spin three gauge transformations. We then construct two other nontrivial Weyl but not gauge invariant actions which are linear in the Weyl tensor of the background geometry. We then discuss existence and uniqueness of a possible linear combination of these three actions which is gauge invariant. We do this at the linear order in the background curvature for Ricci flat backgrounds.Comment: 32 pages, v.2, misprints correcte

Off-shell construction of some trilinear higher spin gauge field interactions

Several trilinear interactions of higher spin fields involving two equal ($s=s_{1}=s_{2}$) and one higher even ($s_{3}\geq 2s$) spin are presented. Interactions are constructed on the Lagrangian level using Noether's procedure together with the corresponding next to free level fields of the gauge transformations. In certain cases when the number of derivatives in the transformation is $2s-1$ the interactions lead to the currents constructed from the generalization of the gravitational Bell-Robinson tensors. In other cases when the number of derivatives in the transformation is more than $2s-1$ we obtain the finite tower of interactions with smaller even spins less than $s_{3}$ in full agreement with our previous results for the interaction of the higher even spins field with a conformal scalar [1,2].Comment: 21 pages, latex, v.2, minor corrections, ref. added, v.3 accepted in Nucl. Phys.

General trilinear interaction for arbitrary even higher spin gauge fields

Using Noether's procedure we present a complete solution for the trilinear interactions of arbitrary spins $s_{1},s_{2}, s_{3}$ in a flat background, and discuss the possibility to enlarge this construction to higher order interactions in the gauge field. Some classification theorems of the cubic (self)interaction with different numbers of derivatives and depending on relations between the spins are presented. Finally the expansion of a general spin $s$ gauge transformation into powers of the field and the related closure of the gauge algebra in the general case are discussed.Comment: 21 pages, Latex, v.2. minor correction,v.3 final correction

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.

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.

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

Electrically charged black branes in N=4^+, D=5 gauged supergravity

We analyze the properties of asymptotically AdS electrically charged black brane solutions in a consistent truncation of the N=4^+, D=5 Romans' gauged supergravity which contains gravity, SU(2) and U(1) gauge fields, and a dilaton possessing a nontrivial potential approaching a constant negative value at infinity. We find that the U(1)\times U(1) solutions become unstable to forming non-Abelian hair. These configurations emerge as zero modes of the Abelian solutions at critical temperature and a critical (nonvanishing) ratio of the electric charges and can be viewed as holographic p-wave superfluids.Comment: 12 pages, 4 figure