# On Covariant Actions for Chiral $p-$Forms

## TL;DR

This paper develops a covariant, polynomial action for free chiral p-forms, extending the PST formulation, and demonstrates duality symmetries including in duality-symmetric electromagnetic theories.

## Contribution

It introduces a new covariant action for chiral p-forms with duality symmetries, including a duality-symmetric electromagnetic formulation with multiple gauge fields.

## Key findings

- Constructed a Lorentz covariant action equivalent to PST formulation.
- Demonstrated duality symmetries in the new action.
- Applied the formulation to duality-symmetric electromagnetism.

## Abstract

We construct a Lorentz and generally covariant, polynomial action for free chiral $p-$forms, classically equivalent to the Pasti-Sorokin-Tonin (PST) formulation. The minimal set up requires introducing an auxiliary $p-$form on top of the physical gauge $p-$form and the PST scalar. The action enjoys multiple duality symmetries, including those that exchange the roles of physical and auxiliary $p-$form fields. Actions of the same type are available for duality-symmetric formulations, which is demonstrated on the example of the electromagnetic field in four dimensions. There, the degrees of freedom of a single Maxwell field are described employing four distinct vector gauge fields and a scalar field.