Tensor Galileons as Lovelock theories

TL;DR

This paper explores the construction of Galileon interactions for mixed-symmetry tensors, revealing their correspondence to Lovelock gravity theories through a geometric tensor approach.

Contribution

It introduces a systematic method to derive Galileon theories for mixed-symmetry tensors using Riemann-like tensors, connecting them to Lovelock gravity.

Findings

Galileon interactions for mixed-symmetry tensors are constructed.

These theories correspond to known Galileon models in the literature.

A geometric tensor framework links Galileons to Lovelock gravity.

Abstract

We review the construction of Galileon interactions involving a single two-column mixed-symmetry tensor of arbitrary degree in flat spacetime of arbitrary dimensions, in a reverse engineering spirit. By defining an appropriate Riemann-like tensor for each of these tensor gauge fields, we show that the theories constructed in the spirit of Lovelock's theory of Gravity correspond to the well-known Galileon theories from the literature.