The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.
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ArXiv ePrint: 1612.05991
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Chatzistavrakidis, A., Khoo, F.S., Roest, D. et al. Tensor Galileons and gravity. J. High Energ. Phys. 2017, 70 (2017). https://doi.org/10.1007/JHEP03(2017)070