Exact duality in the string effective action

Abstract

We formulate $\sigma$-model duality transformations in terms of spin connection. This allows one to investigate the symmetry of the string action including higher order ${\alpha }^{\prime }$ corrections. An important feature of the new duality transformations is a simple homogeneous transformation rule of the spin connection (with torsion) and specifically adjusted transformation of the Yang-Mills field. We find that under certain conditions this duality is a symmetry of the full effective string action in the target space, free of ${\alpha }^{\prime }$ corrections. We demonstrate how the exact duality generates new fundamental string solutions from supersymmetric string waves.