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On the moduli space curvature at infinity
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On the moduli space curvature at infinity
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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.
Forward citations
Cited by 4 Pith papers
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On Quantum Obstructions in Type IIA Orientifolds
Quantum corrections obstruct infinite distance limits in Type IIA orientifold Kähler moduli unless other moduli are also taken to infinity, as shown by worldsheet EFT strings, massless towers, and M-theory G2 uplifts.
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Quantum Gravity Cutoff from Axions: A Type IIB Landscape Study
The bound Λ_QG ≲ 2π √S f holds for C2 and C4 axions in Type IIB Calabi-Yau compactifications even near Kähler moduli space boundaries where co-scaling fails.
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Gravity Decoupling and Axionic Shift Symmetries
Axionic string tensions define vector fields on moduli space that split into mutually orthogonal subsets with one decoupling from gravity, and their Laplacian relates to divergent moduli space curvature.
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Sharpening the Supersymmetric Axion Weak Gravity Conjecture
The paper verifies the bound fS/|n| ≤ (π/(2 κ_d)) sqrt((d-1)/(d-2)) for axion instantons and sharpens it to fS/|n| ≤ (1/κ_4) sqrt(7/2) for supersymmetric 4d instantons using three approaches in the string landscape.
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