Swampland Bounds on the Abelian Gauge Sector

TL;DR

This work derives universal swampland bounds on the number of abelian gauge factors in six-dimensional ${\mathcal N}=(1,0)$ supergravities and their F-theory realizations by enforcing the unitarity and consistency of BPS strings coupled to tensor multiplets. The authors show a general bound $N\le c_L$ in supergravity, yielding $N\le32$ for $T=0$ and $N\le20$ for $T=1$, with a stronger geometric bound $N\le16$ for any F-theory model with $T\ge1$ via a heterotic solitonic string, an result that extends to certain four-dimensional F-theory vacua. They relate abelian charges to height pairings and the Mordell–Weil group, obtaining a universal bound on the rank of the Mordell–Weil group of elliptic Calabi–Yau threefolds. The findings imply that abelian sectors in 6d F-theory models with tensor multiplets embed into $E_8\times E_8$ and offer conjectures for extensions to 4d and for bases like $\mathbb P^2$, with implications for the structure of allowed charge spectra.

Abstract

We derive bounds on the number of abelian gauge group factors in six-dimensional gravitational theories with minimal supersymmetry and in their F-theoretic realisations. These bounds follow by requiring consistency of certain BPS strings in the spectrum of the theory, as recently proposed in the literature. Under certain assumptions this approach constrains the number of abelian gauge group factors in six-dimensional supergravity theories with at least one tensor multiplet to be $N \leq 20$ (or $N \leq 22$ in absence of charged matter). For any geometric F-theory realisation with at least one tensor multiplet we establish the bound $N \leq 16$ by demanding unitarity of a heterotic solitonic string which exists even in absence of a perturbative heterotic dual. This result extends to four-dimensional F-theory vacua on any blowup of a rational fibration. Our findings lead to universal bounds on the rank of the Mordell-Weil group of elliptically fibered Calabi-Yau threefolds.