String theory at order $\alpha'^2$ and the generalized Bergshoeff-de Roo identification

TL;DR

This paper investigates second-order 1-corrections in string theory within Double Field Theory, providing evidence that a generalized Bergshoeff-de Roo identification correctly captures these corrections for bosonic and heterotic strings.

Contribution

It demonstrates that the extended DFT formalism with a generalized Bergshoeff-de Roo identification accurately reproduces 1^2-corrections, including the Riemann cubed term for bosonic strings.

Findings

1^2-corrections include a cubic Riemann term for bosonic strings

The approach aligns with known correction structures and coefficients

Provides evidence for the validity of the generalized identification at second order

Abstract

It has been shown by Marques and Nunez that the first $\alpha'$-correction to the bosonic and heterotic string can be captured in the $O(D,D)$ covariant formalism of Double Field Theory via a certain two-parameter deformation of the double Lorentz transformations. This deformation in turn leads to an infinite tower of $\alpha'$-corrections and it has been suggested that they can be captured by a generalization of the Bergshoeff-de Roo identification between Lorentz and gauge degrees of freedom in an extended DFT formalism. Here we provide strong evidence that this indeed gives the correct $\alpha'^2$-corrections to the bosonic and heterotic string by showing that it leads to a cubic Riemann term for the former but not for the latter, in agreement with the known structure of these corrections including the coefficient of Riemann cubed.