On the moduli space curvature at infinity

TL;DR

This paper classifies the divergence of scalar curvature in the vector multiplet moduli space of type IIA string theory on Calabi-Yau manifolds, linking geometric and physical causes of divergence and its relation to decoupled field theories.

Contribution

It provides a comprehensive classification of asymptotic scalar curvature behaviour in moduli spaces and connects divergences to decoupled non-gravitational field theories.

Findings

Scalar curvature diverges positively along certain infinite distance trajectories.

Divergences are caused by effective divisors with fixed volume in the limit.

Decoupled field theories exhibit non-zero rigid moduli space curvature.

Abstract

We analyse the scalar curvature of the vector multiplet moduli space $\mathcal{M}^{\rm VM}_X$ of type IIA string theory compactified on a Calabi--Yau manifold $X$. While the volume of $\mathcal{M}^{\rm VM}_X$ is known to be finite, cases have been found where the scalar curvature diverges positively along trajectories of infinite distance. We classify the asymptotic behaviour of the scalar curvature for all large volume limits within $\mathcal{M}^{\rm VM}_X$, for any choice of $X$, and provide the source of the divergence both in geometric and physical terms. Geometrically, there are effective divisors whose volumes do not vary along the limit. Physically, the EFT subsector associated to such divisors is decoupled from gravity along the limit, and defines a rigid $\mathcal{N}=2$ field theory with a non-vanishing moduli space curvature $R_{\rm rigid}$. We propose that the relation between scalar curvature divergences and field theories that can be decoupled from gravity is a common trait of moduli spaces compatible with quantum gravity.