First Order Actions and Duality

TL;DR

This paper explores classical S-duality transformations within first order actions, revealing their reformulation as canonical local transformations and analyzing their implications for electromagnetic duality and string theory.

Contribution

It demonstrates that electromagnetic duality can be expressed as a canonical local transformation in first order actions and extends the analysis to string theory dualities.

Findings

Electromagnetic duality is a canonical local transformation in first order actions.

Dualities relate actions with different kinetic terms in the reduced phase space.

Dualities are not canonical transformations for the Dirac bracket.

Abstract

We consider some aspects of classical S-duality transformations in first order actions taken into account the general covariance of the Dirac algorithm and the transformation properties of the Dirac bracket. By classical S-Duality transformations we mean a field redefinition that interchanges the equations of motion and its associated Bianchi identities. By working from a first order variational principle and performing the corresponding Dirac analysis we find that the standard electro-magnetic duality can be reformulated as a canonical local transformation. The reduction from this phase space to the original phase space variables coincides with the well known result about duality as a canonical non local transformation. We have also applied our ideas to the bosonic string. These Dualities are not canonical transformations for the Dirac bracket and relate actions with different kinetic terms in the reduced space.