EFT strings and dualities in 4d $\mathcal{N}=1$

Abstract: We investigate the global structure of the states becoming light at perturbative limits of 4d $\mathcal{N}=1$ string and M-theory compactifications, identifying the different duality frames that emerge asymptotically and how they fit together in moduli space. These limits are characterized by the presence of EFT strings - a special class of axionic BPS strings whose tension, derived from the IR K\"ahler potential, vanishes in Planck units at infinite field distance. An intriguing integer scaling relation, $m \sim \mathcal{T}^w$ with $w = {1,2,3}$ in Planck units, connects the tension $\mathcal{T}$ of these strings to the mass scale $m$ of the leading tower of states along the string flow. We show that this relation also holds for the subleading towers below the species scale that generate the tower convex hull, implying that their associated $\vec\zeta = -\vec{\nabla} \log m$ vectors lie in a lattice generated by those of the EFT strings. This reveals a striking UV/IR interplay and offers organizing principles for the parametric hierarchies among the relevant UV scales in a given perturbative limit and the web of dualities governing 4d string vacua.