The $\alpha'^2$ correction from double field theory

TL;DR

This paper derives the order α'^2 correction to the double field theory action for string effective actions, simplifying previous proposals and confirming consistency with known heterotic string results.

Contribution

It provides a direct calculation of the α'^2 correction in DFT, resulting in a simpler form and establishing its relation to existing all-order proposals.

Findings

Derived the α'^2 correction to DFT action.

Confirmed the correction reproduces heterotic string results.

Simplified the form of the correction compared to previous work.

Abstract

It is known that the order $\alpha'$ 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 $\alpha'^2$ by a direct calculation. The result is vastly simpler than previous proposals. We show that this correction reproduces the known $\alpha'^2$ 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.