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We unveil a remarkable interplay between rigid field theories (RFTs), charge-to-mass ratios $\gamma$ and scalar curvature divergences $\mathsf{R}_{\rm div}$ in the vector multiplet moduli space of 4d ${\cal N}=2$ supergravities, obtained upon compactifying type II string theory on Calabi--Yau threefolds. We show that the condition to obtain an RFT that decouples from gravity implies a divergence in the $\gamma$ of (would-be) BPS particles charged under the rigid theory, and vice-versa. For weak coupling limits, where the scalar curvature diverges, we argue that such BPS particles exist and that $\mathsf{R}_{\rm div} \lesssim \gamma^2$, implying that all these divergences are a consequence of RFT limits. More precisely, along geodesics we find that $\mathsf{R}_{\rm div} \sim (\Lambda_{\rm wgc}/\Lambda_g)^2$, where $\Lambda_{\rm wgc} \equiv g_{\rm rigid} M_{\rm Pl}$ is the RFT cut-off estimate of the Weak Gravity Conjecture and $\Lambda_g = g_{\rm rigid}^{-2} \Lambda_{\rm RFT}$ the electrostatic energy integrated up to its actual cut-off $\Lambda_{\rm RFT}$., Comment: 8 pages; v2: minor modifications and clarifications added

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 $R \sim (\Lambda_{\rm WGC}/\Lambda_{\rm sp})^{2\nu}$, with $\Lambda_{\rm WGC} \equiv g_{\rm rigid} M_{\rm P}$ and $\Lambda_{\rm sp}$ 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 $\nu$, and it either corresponds to a 5d SCFT, 6d SCFT or a Little String Theory., Comment: 56 pages, 5 figures, 2 tables

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., Comment: 43 pages + appendices, 3 figures, table 1 simplified, typos corrected

We revisit the Emergence Proposal in 4d ${\cal N}=2$ vector multiplet sectors that arise from type II string Calabi--Yau compactifications, with emphasis on the role of axionic fundamental strings, or EFT strings. We focus on large-volume type IIA compactifications, where EFT strings arise from NS5-branes wrapping internal four-cycles, and consider a set of infinite-distance moduli-space limits that can be classified in terms of a scaling weight $w=1,2,3$. It has been shown before how one-loop threshold effects of an infinite tower of BPS particles made up of D2/D0-branes generate the asymptotic behaviour of the gauge kinetic functions along limits with $w=3$. We extend this result to $w=2$ limits, by taking into account D2-brane multi-wrapping numbers. In $w=1$ limits the leading tower involves EFT string oscillations, and one can reproduce the behaviour of both weakly and strongly-coupled $U(1)$'s independently on whether the EFT string is critical or not, by assuming that charged modes dominate the light spectrum., Comment: 33 pages + 2 appendices, references and an appendix added

There exists no natural variational principle for the dynamics of abelian p-form potentials with self-dual field strengths, also called chiral p-forms. Relying on the PST method, we establish the general consistency condition for a Lagrangian to describe a Lorentz invariant self-interacting chiral 2n-form in 4n+2 dimensions. For a generic n, we determine a canonical solution of this condition for a quartic interaction Lagrangian of the 2n-form, and prove that for the four-form in ten dimensions this interaction is unique. It generalizes the corresponding Born-Infeld-like interaction of a chiral two-form in six dimensions. We verify that under a dimensional reduction on a torus, this interaction Lagrangian reduces to a combination of the two recently constructed SO(2)-duality invariant quartic interactions for abelian three-form potentials in eight dimensions. The potential relevance of our method for the type IIB superstring effective action is discussed., Comment: 19 pages, references added, typos corrected

We analyze non-linear interactions of 2N-form Maxwell fields in a space-time of dimension D=4N. Based on the Pasti-Sorokin-Tonin (PST) method, we derive the general consistency condition for the dynamics to respect both manifest SO(2)-duality invariance and manifest Lorentz invariance. For a generic dimension D=4N, we determine a canonical class of exact solutions of this condition, which represent a generalization of the known non-linear duality invariant Maxwell theories in D=4. The resulting theories are shown to be equivalent to a corresponding class of canonical theories formulated a la Gaillard-Zumino-Gibbons-Rasheed (GZGR), where duality is a symmetry only of the equations of motion. In dimension D=8, via a complete solution of the PST consistency condition, we derive new non-canonical manifestly duality invariant quartic interactions. Correspondingly, we construct new non-trivial quartic interactions also in the GZGR approach, and establish their equivalence with the former. In the presence of charged dyonic p-brane sources, we reveal a basic physical inequivalence of the two approaches. The power of our method resides in its universal character, reducing the construction of non-linear duality invariant Maxwell theories to a purely algebraic problem., Comment: 43 pages, title changed, references added, typos corrected