Species scale, worldsheet CFTs and emergent geometry

Abstract: We study infinite-distance limits in the moduli space of perturbative string vacua. The remarkable interplay of string dualities seems to determine a highly non-trivial dichotomy, summarized by the emergent string conjecture, by which in some duality frame either internal dimensions decompactify or a unique critical string becomes tensionless. We investigate whether this pattern persists in potentially non-geometric settings, showing that (a proxy for) the cutoff of the gravitational effective field theory in perturbative type II vacua extracted from a graviton scattering amplitude vanishes if and only if a light tower of states appears. Moreover, under some technical assumptions on the spectrum of conformal weights, the cutoff scales with the spectral gap of the internal conformal field theory in the same manner as in decompactification or emergent string limits, regardless of supersymmetry or whether the internal sector is geometric. As a byproduct, we elucidate the role of the species scale in (de)compactifications and show compatibility between effective field theory and worldsheet approaches in geometric settings with curvature.