On covariant actions for chiral p-forms

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. Same type of actions are available for duality-symmetric formulations, which is demonstrated on the example of 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.