A Note on Modular Invariant Species Scale and Potentials

Abstract The species scale provides an upper bound for the ultraviolet cutoff of effective theories of gravity coupled to a number of light particle species. Modular invariant (super‐)potentials provide a simple and computable expression of the species scale as a function of the moduli in toroidal orbifold compactifications of type II and heterotic string are pointed out. Due t o modular symmetry, these functions are valid over all moduli space and not only in asymptotic regions. Additive logarithmic corrections to the species scale arise from the requirement that the latter be modular invariant are observed. The moduli‐dependent expression of the species scale in terms of the gravitino mass or the scalar potential of these models are recasted and swampland conjectures such as the anti‐de Sitter distance conjecture and the gravitino conjecture are connected.