Moduli-dependent species scale

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, 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 Λ sp ∼ 1 √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.