Abstract
To compute the string one-loop correction to the Kähler potential of moduli fields of string compactifications in Einstein-frame, one must compute: the string one-loop correction to the Einstein-Hilbert action, the string one-loop correction to the moduli kinetic terms, the string one-loop correction to the definition of the holomorphic coordinates. In this note, in the small warping limit, we compute the string one-loop correction to the Einstein-Hilbert action of type II string theory compactified on orientifolds of Calabi-Yau threefolds. We find that the one-loop correction is determined by the new supersymmetric index studied by Cecotti, Fendley, Intriligator, and Vafa and the Witten index. As a simple application, we apply our results to estimate the size of the one-loop corrections around a conifold point in the Kähler moduli space.
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Acknowledgments
The work of MK was supported by a Pappalardo fellowship. We thank the referee for valuable suggestions that improved the draft significantly. MK thanks Atakan Hilmi Fırat, Liam McAllister, Mehmet Demirtas, Wati Taylor, Daniel Junghans, Gerben Venken, Arthur Hebecker, Harold Erbin, Xi Yin, Ying-Hsuan Lin, and Simon Schreyer for the discussions. MK thanks Patrick Jefferson, Michael Haack, and Marcus Berg for comments on the draft. MK thanks Daniel Harlow and Hirosi Ooguri for their encouragement.
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Kim, M. On string one-loop correction to the Einstein-Hilbert term and its implications on the Kähler potential. J. High Energ. Phys. 2023, 44 (2023). https://doi.org/10.1007/JHEP07(2023)044
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DOI: https://doi.org/10.1007/JHEP07(2023)044