Duality of Self-Dual Actions

TL;DR

This paper explores duality properties of actions describing chiral bosons, introducing a new covariant duality-symmetric Maxwell action with a two-form auxiliary field, and analyzing its self-duality and coupling to sources.

Contribution

It presents a novel covariant duality-symmetric Maxwell action involving a two-form auxiliary field, extending previous formulations and analyzing its properties and dualities.

Findings

Derived a new covariant duality-symmetric Maxwell action.

Showed the action reduces to Zwanziger's form under gauge fixing.

Demonstrated self-duality of the formulations with respect to field-strength dualization.

Abstract

Using examples of a D=2 chiral scalar and a duality-symmetric formulation of D=4 Maxwell theory we study duality properties of actions for describing chiral bosons. In particular, in the D=4 case, upon performing a duality transform of an auxiliary scalar field, which ensures Lorentz covariance of the action, we arrive at a new covariant duality-symmetric Maxwell action, which contains a two-form potential as an auxiliary field. When the two-form field is gauge fixed this action reduces to a duality-symmetric action for Maxwell theory constructed by Zwanziger. We consider properties of this new covariant action and discuss its coupling to external dyonic sources. We also demonstrate that the formulations considered are self-dual with respect to a dualization of the field-strengths of the chiral fields.