Asymptotic curvature divergences and non-gravitational theories

A bstract We analyse divergences of the scalar curvature R of the vector multiplet moduli space of type IIA string theory compactified on a Calabi-Yau X , along infinite-distance large volume limits. Extending previous results, we classify the origin of the divergence along trajectories which implement decompactifications to F-theory on X and/or emergent heterotic string limits. In all cases, the curvature divergence can be traced back to a 4d rigid field theory that decouples from gravity along the limit. This can be quantified via the asymptotic relation R ~ (Λ WGC / Λ sp ) 2 ν , with Λ WGC ≡ g rigid M P and Λ sp the species scale. In the UV, the 4d rigid field theory becomes a higher-dimensional, strongly-coupled rigid theory that also decouples from gravity. The nature of this UV theory is encoded in the exponent ν , and it either corresponds to a 5d SCFT, 6d SCFT or a Little String Theory.