The α′2 correction from double field theory

Abstract

It is known that the order α′ correction to the tree-level effective action for the bosonic and heterotic string can be described in the framework of Double Field Theory (DFT). Here we determine the DFT action and transformations at order α′2 by a direct calculation. The result is vastly simpler than previous proposals. We show that this correction reproduces the known α′2 correction to the heterotic string effective action. The relation of our action to an (implicit) all order proposal coming from the so-called generalized Bergshoeff-de Roo identification is also discussed.