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

Abstract

It has been shown by Marques and Nunez that the first ${\alpha }^{\prime }$-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 ${\alpha }^{\prime }$-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 ${\alpha }^{\prime 2}$-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.

arXiv comment13 pages; v2: Clarifications added. Published version

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• Higher-derivative Heterotic Kerr-Sen Black Holes
• Duality covariant field redefinitions