Arbitrary p-form Galileons

TL;DR

This paper generalizes scalar Galileon theories to arbitrary even p-forms, constructing actions with second-order field equations involving mixed p-forms, including in curved space.

Contribution

It introduces a systematic way to build second-order p-form Galileon actions, extending previous scalar-only models to include mixed and higher p-forms in various dimensions.

Findings

Constructed explicit actions for arbitrary p-forms with second-order equations

Demonstrated curved-space generalizations with non-minimal couplings

Provided examples of pure and mixed p-form Galileon theories

Abstract

We show that scalar, 0-form, Galileon actions --models whose field equations contain only second derivatives-- can be generalized to arbitrary even p-forms. More generally, they need not even depend on a single form, but may involve mixed p combinations, including equal p multiplets, where odd p-fields are also permitted: We construct, for given dimension D, general actions depending on scalars, vectors and higher p-form field strengths, whose field equations are of exactly second derivative order. We also discuss and illustrate their curved-space generalizations, especially the delicate non-minimal couplings required to maintain this order. Concrete examples of pure and mixed actions, field equations and their curved space extensions are presented.