Abstract
It has been shown by Marques and Nunez that the first α′-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 α′-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 α′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.
Highlights
JHEP11(2021)186 in [13] take a very complicated form and it was not possible to compare them to the known corrections to the bosonic and heterotic string
Stanislav Hronek and Linus Wulff Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, 611 37 Brno, Czech Republic E-mail: 436691@mail.muni.cz, wulff@physics.muni.cz. It has been shown by Marques and Nunez that the first α -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 α -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
Summary
We will use the expressions given in [13], but it is important to remember that their action differs from ours by an overall factor of 2. We use a subscript to distinguish different types of terms mostly according to the projections involved. Terms of third order in fields not containing FA and with the following projections (up to the section condition) ∂(+)∂(+)∂(+)F (−)F (−)F (−):. Terms of third order in fields without FA with projections of the type ∂(+)∂(+)∂(+) · F (−)F (−)F (−): R(&Φ1,1). Terms of third order in fields without FA with projections of the type ∂(+)∂(+)∂(−) · F (−)F (−)F (+): eF f de FddeFef f deFdde. Recall that due to the difference in conventions compared to [13] the expression in our conventions should be twice this
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