Note on manifest Lorentz and general coordinate invariance in duality symmetric models

We consider a generalization of a duality symmetric model proposed by Schwarz and Sen [J.H. Schwarz and A. Sen, Nucl. Phys. B 411 (1994) 35]. It is based on enlarging the model with a dynamical vector field being a time-like component of a local Lorentz frame. This allows one to preserve the manifest Lorentz invariance of the model in flat space-time. The presence of this field is regarded as a relic of gravitational interaction which respects the general coordinate invariance in curved space-time but breaks the local Lorentz symmetry in tangent space down to its spacial subgroup.