Duality in Gauge Theory, Gravity and String Theory

Einstein's theory in the vacuum was recently shown to possess an $SO(2)$ duality invariance, which is broken by coupling to matter. Duality invariance can be restored by enlarging the phase space of the theory to allow for violations of the algebraic Bianchi identity. We show that in cases where the matter content can be understood as a component of the torsion tensor duality can be restored and we compute the corresponding duality current. We consider the case of NS-NS gravity as an example and find that the duality current is given by the divergence of the axion. In the linearized approximation of the low energy heterotic string theory these results imply that duality of the generalized Riemann curvature tensor implements Riemannian, axion-dilaton and electro-magnetic dualities simultaneously.