First Order Actions and Duality
  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. 
Alejandro Gaona and J. Antonio Garcia