A note on modular invariant species scale and potentials

Understand

The species scale provides an upper bound for the ultraviolet cutoff of effective theories of gravity coupled to a number of light particle species.

• We point out that 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.
• Due to modular symmetry, these functions are valid over all moduli space and not only in asymptotic regions.
• We observe that additive logarithmic corrections to the species scale arise from the requirement that the latter be modular invariant.