Note on antisymmetric spin-tensors

Abstract

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.

7 pages, no figures

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• Frame-like gauge invariant formulation for mixed symmetry fermionic fields
• Fermionic Higher-form Symmetries
• On the quantisation and anomalies of antisymmetric tensor-spinors
• Supersymmetric action for 6D $(4,0)$ supergravity
• Fermionic Shift Symmetries in (Anti) de Sitter Space
• Dynamical spectral structure of density fluctuation near QCD critical point
• On gauge-invariant deformation of reducible gauge theories