Abstract
In this note, we prove that the one-loop pfaffian of the non-perturbative superpotential generated by Euclidean D-branes in type II compactifications on orientifolds of Calabi-Yau threefolds is determined by the moduli integral of the new supersymmetric index defined by Cecotti, Fendley, Intriligator, and Vafa. As this quantity can be computed via topological string theory, Chern-Simons theory, matrix models, or by solving the holomorphic anomaly equation, this result provides a method to directly compute the one-loop pfaffian of the non-perturbative superpotential. The relation between the one-loop pfaffian, threshold corrections to the gauge coupling, and the one-loop partition function of open topological string theory is discussed.
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Acknowledgments
The work of MK was supported by the Pappalardo fellowship. We thank Ashoke Sen and Sergei Alexandrov for their valuable comments. We thank Sergei Alexandrov for catching typos in the manuscript. We thank Atakan Hilmi Fırat, Liam McAllister, Jakob Moritz, and Andreas Schachner for discussions.
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Kim, M. D-instanton, threshold corrections, and topological string. J. High Energ. Phys. 2023, 97 (2023). https://doi.org/10.1007/JHEP05(2023)097
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DOI: https://doi.org/10.1007/JHEP05(2023)097