Moduli-dependent Species Scale

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, $\mathcal{N}=2$ theories, using the one loop topological free energy $F_1$, which we relate to a gravitational version of the $a$-function. This leads to ${\Lambda }_{\mathrm{sp}}\sim 1/\sqrt{F_1}$ 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.

28 pages, 7 figures

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• Emergent Strings in Type IIB Calabi--Yau Compactifications
• EFT & Species Scale: Friends or foes?
• Bulk/boundary Modular Quintessence and DESI
• Black Hole Entropy, Quantum Corrections and EFT Transitions
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Inflationary constraints on the moduli-dependent species scale in modular invariant theories
• The CFT Distance Conjecture and Tensionless String Limits in $\mathcal{N}=2$ Quiver Gauge Theories
• Center Symmetry Breaking in Calabi--Yau Compactifications
• Background instability of quintessence model in light of entropy and distance conjecture
• Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape