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

TL;DR

This paper investigates the scalar curvature behavior in the moduli space of 5d $ abla$1 supergravity theories derived from M-theory compactifications, revealing that divergences occur at points where gauge interactions become infinitely strong, indicating decoupled SCFTs or LSTs.

Contribution

It identifies the precise conditions under which curvature divergences occur in 5d $ abla$1 supergravity moduli spaces, linking them to infinite coupling limits and the emergence of SCFTs or LSTs.

Findings

Curvature $R$ diverges at infinite coupling points.

Divergences relate to decoupled SCFTs or LSTs.

Additional conditions for rank $r\, extless=2$ SCFTs.

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.