Curvature divergences in 5d $\mathcal{N} = 1$ supergravity

Abstract

We study the scalar curvature $R$ of the vector moduli space of 5d $\mathcal{N}=1$ supergravities, obtained by compactifying M-theory on a Calabi--Yau three-fold. We find that $R$ can only diverge at points where some gauge interactions go to infinite coupling in Planck units and become SCFTs or LSTs decoupled from gravity and other vector multiplets. For 5d SCFTs of rank $r\leq 2$ divergences occur if, additionally, the SCFT still couples to the vevs of such vector multiplets, so that along its Coulomb branch its gauge kinetic matrix and/or string tensions depend on some non-dynamical parameters. If the strong coupling singularity is better understood as a 6d $(1,0)$ SCFT, as in some decompactification limits, then divergences in $R$ arise when the SCFT is endowed with a non-Abelian gauge group.