On p-form theories with gauge invariant second order field equations

TL;DR

This paper classifies p-form theories with second order gauge invariant equations, extending Galileon models, and constructs a non-trivial gauge invariant 3-form theory with polynomial action, challenging previous no-go results.

Contribution

It provides a general classification method for such theories, establishes bounds on their number, and constructs a novel gauge invariant 3-form Galileon-like theory with a polynomial action.

Findings

Classified extensions of p-form Galileon theories with second order equations.

Established an upper bound on the number of such theories based on p and spacetime dimension.

Constructed a non-trivial gauge invariant 3-form theory with polynomial derivatives, countering previous no-go theorems.

Abstract

We explore field theories of a single p-form with equations of motions of order strictly equal to two and gauge invariance. We give a general method for the classification of such theories which are extensions to the p-forms of the Galileon models for scalars. Our classification scheme allows to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a non trivial Galileon like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no non trivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd p cases.