Is every infinite-distance limit a decompactification or a weak string?
In plain words
Some parameters of string theory can be pushed infinitely far, and then a tower of particles becomes very light. A conjecture says the light tower is always either extra dimensions opening up or a new weakly interacting string, with no third option.
Precise statement
Emergent string conjecture (Lee, Lerche, Weigand 2019): in any infinite-distance limit in the moduli space of a d-dimensional quantum gravity theory, the leading tower of states becoming massless in Planck units is either a Kaluza-Klein tower (decompactification) or the excitation tower of a unique weakly coupled, asymptotically tensionless critical string. Prove this from general principles or find a limit whose leading tower is of another kind.
What would settle it
A derivation from black-hole thermodynamics and unitarity valid for every infinite-distance limit, or an explicit compactification with a light leading tower of another kind.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Verified in vector-multiplet moduli spaces of M-theory and type IIA on Calabi-Yau threefolds (2019), in 5D supergravity limits (2024), and argued from the black-hole density of states (Bedroya, Mishra, Wiesner 2024); no general proof.
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