Abstract
We confirm the leading α ′3 correction to the 4d, \( \mathcal{N}=1 \) Kähler potential of type IIB orientifold compactifications, proportional to the Euler characteristic of the Calabi-Yau threefold (BBHL correction). We present the explicit solution for the α ′3-modified internal background metric in terms of the non-harmonic part of the third Chern form of the leading order Calabi-Yau manifold. The corrected internal manifold is almost Calabi-Yau and admits an SU(3) structure with non-vanishing torsion. We also find that the full ten-dimensional Einstein frame background metric is multiplied by a non-trivial Weyl factor. Performing a Kaluza-Klein reduction on the modified background we derive the α ′3-corrected kinetic terms for the dilaton and the Kähler deformations of the internal Calabi-Yau threefold for arbitrary h 1,1. We analyze these kinetic terms in the 4d, \( \mathcal{N}=2 \) un-orientifolded theory, confirming the expected correction to the Kähler moduli space pre-potential, as well as in the 4d, \( \mathcal{N}=1 \) orientifolded theory, thus determining the corrections to the Kähler potential and Kähler coordinates.
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Bonetti, F., Weissenbacher, M. The Euler characteristic correction to the Kähler potential — revisited. J. High Energ. Phys. 2017, 3 (2017). https://doi.org/10.1007/JHEP01(2017)003
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DOI: https://doi.org/10.1007/JHEP01(2017)003