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

Alejandro Blanco, Fernando Marchesano, Luca Melotti

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.

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

Abstract

We study the scalar curvature of the vector moduli space of 5d supergravities, obtained by compactifying M-theory on a Calabi--Yau three-fold. We find that 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 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 SCFT, as in some decompactification limits, then divergences in arise when the SCFT is endowed with a non-Abelian gauge group.
Paper Structure (19 sections, 147 equations, 2 figures, 2 tables)

This paper contains 19 sections, 147 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. M-theory on Calabi--Yau three-folds
  3. Vector multiplet moduli space
  4. The scalar curvature
  5. Rigid limits and curvature divergences
  6. EFT string limits and growth sectors
  7. BPS strings and rigid limits
  8. RFT sectors and decoupling
  9. The rigid curvature
  10. Finite distance limits
  11. Infinite distance limits
  12. Decompactification limits
  13. Emergent string limits
  14. Examples
  15. KMV conifold
  16. ...and 4 more sections

Figures (2)

  • Figure 1: Genus-zero GV invariants of the KMV conifold in the $\mathbb{P}^2$ (left) and the $\mathbb{F}_1$ phase (right), excluding the direction of the elliptic fibre. The dots represent non-zero GV invariants, while the crosses correspond to vanishing ones Alim:2021vhs. The yellow dots represent the flop curve in each phase. The blue dots represent the curves contained within $\mathbb{P}^2$ and $\mathbb{F}_1$, respectively, and which go to zero area when the base collapses.
  • Figure 2: String tensions coming from M5-brane wrapping different kinds of divisors within the kernel of $w=2$ limits, compared to the 6d Kaluza--Klein scale.