On the species scale, modular invariance and the gravitational EFT expansion

The concept of the species scale as the quantum gravity cut-off has been recently emphasised in the context of the Swampland program. Along these lines, we continue the quest for a precise understanding of its role within effective field theories of gravity as well as a global definition of the latter in case there is enough supersymmetry preserved. To do so, we exploit duality symmetries, the familiar asymptotic dependence imposed by the presence of infinite towers of light states and the known behaviour of higher-curvature corrections to the Einstein-Hilbert action in various String Theory setups. In those cases, we obtain a self-consistent result for the identification of the species scale as the quantum gravity cut-off, but also present some puzzles related to the suppression of certain higher-dimensional operators as well as minor ambiguities that may arise in the deep interior of moduli space.