Quadratic s-Form Field Actions with Semi-bounded Energy

TL;DR

This paper classifies quadratic gauge actions based on s-form fields, exploring their uniqueness and limitations, particularly showing the impossibility of certain kinetic terms in four-dimensional gravity theories.

Contribution

It provides a partial classification of quadratic s-form gauge actions and demonstrates the non-existence of certain kinetic terms in 4D gravity theories.

Findings

Classifies consistent quadratic s-form gauge actions.

Shows the uniqueness of Yang-Mills as a deformation of Maxwell.

Proves the impossibility of adding certain kinetic terms to 4D gravity actions.

Abstract

We give in this paper a partial classification of the consistent quadratic gauge actions that can be written in terms of s-form fields. This provides a starting point to study the uniqueness of the Yang-Mills action as a deformation of Maxwell-like theories. We also show that it is impossible to write kinetic 1-form terms that can be consistently added to other 1-form actions such as tetrad gravity in four space-time dimensions even in the presence of a Minkowskian metric background.