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.

Completing R4 using O(d, d)

“…It is also for this reason that we don't use the manifestly O(d, d) invariant formulation known as Double Field Theory (DFT). While the first and second α ′ correction to the bosonic string can be described in this formalism [12,13,14,15,16,17], it appears to fail for the α ′3 correction [18], so it would not be useful for seeing what is common to all these corrections.…”

“…From this expression one can directly read off the field redefinitions required in the reduced theory for O(d, d) invariance. It should be possible to compare this to the DFT calculation in [17], but we will not do so here. Instead we will try to simplify the Lagrangian we have found as much as we can.…”