Curvature divergences and gravity decoupling in Calabi--Yau rigid limits

TL;DR

This work develops a macroscopic framework for gravity decoupling in 4d ${\cal N}=2$ theories from CY compactifications, distinguishing gravitational, rigid, and core RFT sectors via monodromy and axionic shifts. Central to the approach is the core RFT, a monodromy-invariant subsector of rigid U(1)s that can decouple from gravity when kinetic and Pauli mixings are suppressed, a condition signaled by a divergent moduli-space curvature. The authors show how metric and essential instantons shape rigid limits, linking the curvature criterion to the presence of a gravity-decoupled EFT sector across large complex structure, conifold-like, and Seiberg--Witten limits. They illustrate that curvature divergences provide a robust indicator of decoupling, while Pauli mixing can obstruct decoupling in SW-like limits, depending on the relative scales of the SW tower, species scale, and gravitational cut-offs. Overall, the paper offers a coherent macroscopic picture connecting monodromy, instantons, and curvature to gravity decoupling in ${\cal N}=2$ CY compactifications, with implications for Swampland constraints and rigid UV completions.

Abstract

Four-dimensional $\mathcal{N}=2$ supergravity theories become rigid in gravity-decoupling limits. We study this effect for type II string compactifications on general Calabi--Yau manifolds, focusing on vector-multiplet trajectories whose endpoints exhibit axionic shift symmetries. This comprises field excursions of both finite- and infinite distance, but the latter display specific features due to the appearance of light towers of extremal BPS states, in agreement with Swampland principles. We show that vector multiplets split into two sets: those with gravitational and with rigid mutual interactions, and that only a subset of the latter -- dubbed core RFT -- can fully decouple from gravity. We characterise the core RFT in terms of the axionic shift symmetry, and derive decoupling criteria based on kinetic and Pauli interaction mixing. Our framework is illustrated in large complex structure, conifold-like, and Seiberg--Witten limits. In the last case, Pauli mixing obstructs decoupling whenever the dyonic and extremal BPS towers appear at the same scale. Across all these examples, the decoupling from gravity is signalled by a divergent moduli-space scalar curvature.

Figures (1)

• Figure 1: Mass scales along two different classes of limits approaching the SW point. In scenario I) the field theory scales $(\Lambda_{\rm sw}, m_{\rm W}, m_{\rm mon})$ lie parametrically below the species scale, the decoupling occurs and the moduli space curvature diverges. In scenario II)$m_{\rm mon} \gtrsim \Lambda_{\rm sp}$, there is no decoupling from the gravitational sector as well as no curvature divergence.