8d Supergravity, Reconstruction of Internal Geometry and the Swampland

TL;DR

This work sharpens Swampland constraints for $8$-dimensional $\mathcal{N}=2$ supergravity by analyzing the worldvolume theory of instanton $3$-branes and applying a strengthened cobordism conjecture. The authors show that the $3$-brane Coulomb branch moduli form a compact, special-Kähler space identified with an elliptic $K3$ geometry, enabling a direct link between singular fibers and bulk gauge algebras; this yields concrete bounds that exclude $\mathfrak{g}_2$ and, in turn, supports the String Lamppost Principle in 8d with 16 supercharges. The results provide a geometric mechanism to reconstruct internal compactification data from brane probes and demonstrate consistency with known string constructions while highlighting gaps (notably the absence of known $\mathfrak{g}_2$ realizations). By tying 1-brane current-algebra central charges to a global bound $c_{\mathfrak{g}}\le 18$ (κ=1) or $\le 2$ (κ=0) and translating Kodaira-type singularities into gauge data, the paper offers a concrete, geometry-driven path to map the 8d landscape and its Swampland.

Abstract

We sharpen Swampland constraints on 8d supergravity theories by studying consistency conditions on worldvolume theory of 3-brane probes. Combined with a stronger form of the cobordism conjecture, this leads to the reconstruction of the compact internal geometry and implies strong restrictions on the gauge algebra and on some higher derivative terms (related to the level of the current algebra on the 1-brane). In particular we argue that 8d supergravity theories with $\mathfrak{g}_2$ gauge symmetry are in the Swampland. These results provide further evidence for the string lamppost principle in 8d with 16 supercharges.