Arbitrary p-form Galileons

TL;DR

The paper addresses generalizing scalar Galileon actions to arbitrary even $p$-forms and mixed $p$-form systems, yielding field equations of exactly second derivative order. It constructs flat-space actions for even $p$-forms of the form $I=\u2220 d^D x\, \varepsilon^{μν…} \varepsilon^{αβ…} ω_{μν…} ω_{αβ…} (∂_ρ ω_{γδ…}) (∂_ε ω_{στ…})$, with a bound $(D-p-1)/(p+2)$ on derivative factors and a Galilean invariance under constant shifts; odd $p$-forms are flat-space empty unless treated in mixtures or multiplets. The work further extends to mixed-species actions and even non-Abelian generalizations, yielding second-order equations in flat space and illustrating revival of odd-$p$ actions in mixed/multiplet settings. In curved space, non-minimal curvature couplings are constructed to preserve second-order dynamics, with explicit Δ terms displaying how curvature terms compensate higher derivatives; a vector-model example demonstrates curvature-driven, nontrivial dynamics while maintaining controlled field equations. Overall, the results broaden Galileon-like theories to higher-form fields, enabling stable interactions in higher dimensions and offering potential links to brane constructions and modified gravity models.

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.