Covariant actions for models with non-linear twisted self-duality

TL;DR

This paper develops a covariant, duality-invariant formulation for models with non-linear twisted self-duality, extending previous linear models and ensuring manifest covariance and duality symmetry through auxiliary fields.

Contribution

It generalizes duality-symmetric actions to non-linear models with twisted self-duality, maintaining covariance and duality invariance with a systematic approach.

Findings

Duality-symmetric action invariant under two local symmetries

Self-duality condition recast in a covariant form independent of auxiliary scalar

Framework applicable to supersymmetric extensions

Abstract

We describe a systematic way of the generalization, to models with non-linear duality, of the space-time covariant and duality-invariant formulation of duality-symmetric theories in which the covariance of the action is ensured by the presence of a single auxiliary scalar field. It is shown that the duality-symmetric action should be invariant under the two local symmetries characteristic of this approach, which impose constraints on the form of the action similar to those of Gaillard and Zumino and in the non-covariant formalism. We show that the (twisted) self-duality condition obtained from this action upon integrating its equations of motion can always be recast in a manifestly covariant form which is independent of the auxiliary scalar and thus corresponds to the conventional on-shell duality-symmetric covariant description of the same model. Supersymmetrization of this construction is briefly discussed.