Black hole entropy and moduli-dependent species scale

Understand

We provide a moduli-dependent definition of species scale in quantum gravity based on black hole arguments.

• Concretely, it is derived from of a lower bound on the entropy of extremal black holes with higher curvature corrections, which ensures that the black hole can be reliably described within the effective theory.
• By demanding that our definition coincides with a recent proposal for a moduli-dependent species scale motivated from the topological string, we conclude that the conjecture $\mathcal{Z}_{BH} = |\mathcal{Z}_{\rm top}|^2$ relating the black hole to the topological string partition functions should hold, at least within the regime of validity of our analysis.