# Classifying Galileon $p$-form theories

## TL;DR

This paper classifies all abelian gauge invariant p-form theories with second derivative equations of motion, revealing new theories like a 4-form Galileon in higher dimensions and confirming gauge invariance properties.

## Contribution

It provides a complete classification of p-form Galileon theories, constructs explicit actions in various dimensions, and introduces a new 4-form Galileon cubic theory.

## Key findings

- Explicit actions for p-form Galileons in D≤11
- Discovery of a new 4-form Galileon in D≥8
- Proof that equations depend only on field strengths

## Abstract

We provide a complete classification of all abelian gauge invariant $p$-form theories with equations of motion depending only on the second derivative of the field---the $p$-form analogues of the Galileon scalar field theory. We construct explicitly the nontrivial actions that exist for spacetime dimension $D\leq11$, but our methods are general enough and can be extended to arbitrary $D$. We uncover in particular a new $4$-form Galileon cubic theory in $D\geq8$ dimensions. As a by-product we give a simple proof of the fact that the equations of motion depend on the $p$-form gauge fields only through their field strengths, and show this explicitly for the recently discovered $3$-form Galileon quartic theory.