Polynomial Duality-Symmetric Lagrangians for Free p-Forms

TL;DR

This paper develops polynomial Lagrangians for chiral and general p-forms, emphasizing symmetry, simplicity, and a universal, dimension-independent formalism using differential forms.

Contribution

It introduces a unified, polynomial, duality-symmetric Lagrangian framework for p-forms, extending previous models and simplifying the treatment of symmetries and equations of motion.

Findings

Demonstrates the symmetry and simplicity of the polynomial Lagrangians.

Constructs duality-symmetric Lagrangians for general p-forms.

Provides a universal formalism valid in any dimension.

Abstract

We explore the properties of polynomial Lagrangians for chiral $p$-forms previously proposed by the last named author, and in particular, provide a self-contained treatment of the symmetries and equations of motion that shows a great economy and simplicity of this formalism. We further use analogous techniques to construct polynomial democratic Lagrangians for general $p$-forms where electric and magnetic potentials appear on equal footing as explicit dynamical variables. Due to our reliance on the differential form notation, the construction is compact and universally valid for forms of all ranks, in any number of dimensions.