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arXiv · 2212.06841

Moduli-dependent Species Scale

Damian van de Heisteeg·Cumrun Vafa·Max Wiesner·David H. Wu
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Abstract

The counting of the number of light modes in a gravitational theory is captured by the notion of the `species scale', which serves as an effective UV cutoff below the Planck scale. We propose to define a moduli-dependent species scale in the context of 4d, ${\cal N}=2$ theories, using the one loop topological free energy $F_1$, which we relate to a gravitational version of the $a$-function. This leads to $\Lambda_{\rm sp}\sim 1/\sqrt{F_1}$ from which we recover the expected scaling of the species scale in various corners of the moduli space. Moreover by minimizing $F_1$ we define the center of the moduli space (the `desert point') as a point where the species scale is maximal. At this point the number of light degrees of freedom is minimized.

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Damian van de Heisteeg, Cumrun Vafa, Max Wiesner, David H. Wu. 2022-12-13. Moduli-dependent Species Scale. https://doi.org/10.4310/bpam.2024.v1.n1.a1

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