Abstract
In a quantum theory of gravity, the species scale Λs can be defined as the scale at which corrections to the Einstein action become important or alternatively as codifying the “number of light degrees of freedom”, due to the fact that \( {\Lambda}_s^{-1} \) is the smallest size black hole described by the EFT involving only the Einstein term. In this paper, we check the validity of this picture in diverse dimensions and with different amounts of supersymmetry and verify the expected behavior of the species scale at the boundary of moduli space. This also leads to the evaluation of the species scale in the interior of the moduli space as well as to the computation of the diameter of the moduli space. We also find evidence that the species scale satisfies the bound \( {\frac{\left|\nabla {\Lambda}_s\right|}{\Lambda_s}}^2\le \frac{1}{d-2} \) all over moduli space including the interior.
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Acknowledgments
It is a pleasure to thank Naomi Gendler for collaboration during the initial stages of this work and Alek Bedroya, John Stout, and Houri Tarazi for helpful discussions. This work is supported by a grant from the Simons Foundation (602883,CV), the DellaPietra Foundation, and by the NSF grant PHY-2013858. We thank the 2023 Summer Workshop of the Simons Center for Geometry and Physics for kind hospitality where this work was initiated.
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van de Heisteeg, D., Vafa, C., Wiesner, M. et al. Species scale in diverse dimensions. J. High Energ. Phys. 2024, 112 (2024). https://doi.org/10.1007/JHEP05(2024)112
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DOI: https://doi.org/10.1007/JHEP05(2024)112