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. 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.
Highlights
We construct a Lorentz and generally covariant, polynomial action for free chiral p-forms, classically equivalent to the Pasti-Sorokin-Tonin (PST) formulation
Same type of actions are available for duality-symmetric formulations, which is demonstrated on the example of electromagnetic field in four dimensions
If we were to start with the (d − 2)−form, we would not be able to construct, e.g., the massless scalar field theory with φ4 interaction
Summary
We start with a Lagrangian for a chiral p-form φμ1...μp in d = 2p + 2 dimensions:. While cμ, Rμ1...μp and Gμν are auxiliary fields with fully antisymmetric set of Lorentz indices. Even though the Lagrangian given above is not quadratic in fields, it is quadratic in the physical gauge potential φμ1...μp and can be shown to describe exactly a single chiral degree of freedom, in Minkowski space of 2p + 2 dimensions for even p
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