Abstract
The Riemann curvature correction to the type II supergravity at eightderivative level in string frame is given as \( {e^{{-2\phi }}}\left( {{t_8}{t_8}{R^4}+\frac{1}{4}{\epsilon_8}{\epsilon_8}{R^4}} \right) \). For constant dilaton, it has been extended in the literature to the S-duality invariant form by extending the dilaton factor in the Einstein frame to the non-holomorphic Eisenstein series. For non-constant dilaton, however, there are various couplings in the Einstein frame which are not consistent with the S-duality. By constructing the tensors t 2n from Born-Infeld action, we include the appropriate Ricci and scalar curvatures as well as the dilaton couplings to make the above action to be consistent with the S-duality.
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Garousi, M.R. S-duality constraint on higher-derivative couplings. J. High Energ. Phys. 2014, 100 (2014). https://doi.org/10.1007/JHEP05(2014)100
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DOI: https://doi.org/10.1007/JHEP05(2014)100