Bounds on species scale and the distance conjecture

The species scale ${\Lambda }_s$$\le$ M${}_{pl}$ serves as a UV cutoff in the gravitational sector of an EFT and can depend on the moduli of the theory as the spectrum of the theory varies. It is argued that the dependence of the species scale ${\Lambda }_s$ ($\varphi$) on massless (or light) modes ${\varphi }^i$ satisfies M${}_{pl}^{d-2}$|${\Lambda }_s^{\prime }$/${\Lambda }_s$|${}^2$< $O$(1). This bound is true at all points in moduli space including also its interior. The argument is based on the idea that the short distance contribution of massless modes to gravitational terms in the EFT cannot dramatically affect the black hole entropy. Based on string theory arguments the $O$(1) constant in this bound is expected to be equal to $\frac{1}{d-2}$ as the boundary of the moduli space is approached. However, it turns out that along trajectories going from interior points to the boundaries of moduli space the slope of the species scale can approach its asymptotic value from above, thereby implying that the constant in the bound must be larger than $\frac{1}{d-2}$. The bound on the variation of the species scale also implies that the mass of towers of light modes cannot go to zero faster than exponential in field distance in accordance with the Distance Conjecture. (© 2023 Wiley‐VCH GmbH)