Emergent String Conjecture (ESC) on asymptotic limits in moduli space

Prove the Emergent String Conjecture asserting that any asymptotic limit in moduli space of a quantum gravity theory is realized either as a decompactification limit or as a tensionless-string limit.

Background

The authors employ the Emergent String Conjecture to relate the species scale to either the higher-dimensional Planck scale or the string scale, enabling bounds on the time-variation of the string tension in FLRW backgrounds.

This conjecture is central to their Swampland-inspired argument constraining the dynamics of effective string tensions and the resulting gravitational-wave spectral indices.

References

According to the Emergent String Conjecture (ESC) , any asymptotic limit in moduli space is realised either as a decompactification limit or a tension-less string.

— The gravitational wave landscape of cosmic string networks with varying tension  (2601.10790 - Brunelli et al., 15 Jan 2026) in Section 2.1 (Time-dependent string tension: A Swampland Argument)