Note on antisymmetric spin-tensors

It was known for a long time that in d = 4 dimensions it is impossible to construct the Lagrangian for antisymmetric second rank spin-tensor that will be invariant under the gauge transformations with unconstrained spin-vector parameter. But recently a paper arXiv:0902.1471 appeared where gauge invariant Lagrangians for antisymmetric spin-tensors of arbitrary rank n in d > 2n were constructed using powerful BRST approach. To clarify apparent contradiction, in this note we carry a direct independent analysis of the most general first order Lagrangian for the massless antisymmetric spin-tensor of second rank. Our analysis shows that gauge invariant Lagrangian does exist but in d > 4 dimensions only, while in d = 4 this Lagrangian becomes identically zero. As a byproduct, we obtain a very simple and convenient form of this massless Lagrangian that makes deformation to AdS space and/or massive case a simple task as we explicitly show here. Moreover, this simple form admits natural and straightforward generalization on the case of massive antisymmetric spin-tensors of rank n for d > 2n.Comment: 7 pages, no figure

Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex

We apply a recently presented BRST procedure to construct the Largangian cubic vertex of higher-spin gauge field triplets interacting with massive free scalars. In flat space, the spin-s triplet propagates the series of irreducible spin-s, s-2,..,0/1 modes which couple independently to corresponding conserved currents constructed from the scalars. The simple covariantization of the flat space result is not enough in AdS, as new interaction vertices appear. We present in detail the cases of spin-2 and spin-3 triplets coupled to scalars. Restricting to a single irreducible spin-s mode we uncover previously obtained results. We also present an alternative derivation of the lower spin results based on the idea that higher-spin gauge fields arise from the gauging of higher derivative symmetries of free matter Lagrangians. Our results can be readily applied to holographic studies of higher-spin gauge theories.Comment: 26 pages, v2: references adde