Tensor Galileons and Gravity

TL;DR

This paper introduces a new Grassmannian variable-based formulation of Galileon interactions, extending them to mixed-symmetry tensor fields and exploring their coupling to gravity while preserving second-order equations.

Contribution

It develops an index-free approach to Galileon interactions for complex tensor fields and demonstrates their consistent coupling to gravity with second-order field equations.

Findings

Constructed Galileon interactions for mixed-symmetry tensors.

Extended Galileon symmetry to tensors beyond scalars and p-forms.

Showed that coupling to gravity can be achieved without higher-order derivatives.

Abstract

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.