We study the charge-to-mass ratios of BPS states in four-dimensional $$ \mathcal{N} $$ N = 2 supergravities arising from Calabi-Yau threefold compactifications of Type IIB string theory. We present a formula for the asymptotic charge-to-mass ratio valid for all limits in complex structure moduli space. This is achieved by using the sl(2)-structure that emerges in any such limit as described by asymptotic Hodge theory. The asymptotic charge-to-mass formula applies for sl(2)-elementary states that couple to the graviphoton asymptotically. Using this formula, we determine the radii of the ellipsoid that forms the extremality region of electric BPS black holes, which provides us with a general asymptotic bound on the charge-to-mass ratio for these theories. Finally, we comment on how these bounds for the Weak Gravity Conjecture relate to their counterparts in the asymptotic de Sitter Conjecture and Swampland Distance Conjecture.

The axion Weak Gravity Conjecture implies that when parametrically increasing the axion decay constants, instanton corrections become increasingly important. We provide strong evidence for the validity of this conjecture by studying the couplings of R-R axions arising in Calabi-Yau compactifications of Type IIA string theory. Specifically, we consider all possible infinite distance limits in complex structure moduli space and identify the axion decay constants that grow parametrically in a certain path-independent way. We then argue that for each of these limits a tower of D2-brane instantons with decreasing actions can be identified. These instantons ensure that the convex hull condition relevant for the multi-axion Weak Gravity Conjecture cannot be violated parametrically. To argue for the existence of such instantons we employ and generalize recent insights about the Swampland Distance Conjecture. Our results are general and not restricted to specific examples, since we use general results about the growth of the Hodge metric and the sl(2)-splittings of the three-form cohomology associated to each limit.

We present a novel strategy to systematically study complex-structure moduli stabilization in Type IIB and F-theory flux compactifications. In particular, we determine vacua in any asymptotic regime of the complex-structure moduli space by exploiting powerful tools of asymptotic Hodge theory. In a leading approximation the moduli dependence of the vacuum conditions are shown to be polynomial with a dependence given by sl(2)-weights of the fluxes. This simple algebraic dependence can be extracted in any asymptotic regime, even though in nearly all asymptotic regimes essential exponential corrections have to be present for consistency. We give a pedagogical introduction to the sl(2)-approximation as well as a detailed step-by-step procedure for constructing the corresponding Hodge star operator. To exemplify the construction, we present a detailed analysis of several Calabi-Yau three- and fourfold examples. For these examples we illustrate that the vacua in the sl(2)-approximation match the vacua obtained with all polynomial and essential exponential corrections rather well, and we determine the behaviour of the tadpole contribution of the fluxes. Finally, we discuss the structure of vacuum loci and their relations to several swampland conjectures. In particular, we comment on the realization of the so-called linear scenario in view of the tadpole conjecture.

We classify the necessary and sufficient conditions to obtain the near-horizon geometry of extremal supersymmetric rotating black holes embedded in 11d supergravity which are associated to rotating M2-branes. Such rotating black holes admit an AdS2 near-horizon geometry which is fibered by the transverse spacetime directions. In this paper we allow for the most general fibration over AdS2 with a flux configuration permitting rotating M2-branes. Using G-structure techniques we rewrite the conditions for supersymmetry in terms of differential equations on an eight-dimensional balanced space. The 9d compact internal space is a U(1)-fibration over this 8d base. The geometry is constrained by a master equation reminiscent of the one found in the non-rotating case. We give a Lagrangian from which the equations of motion may be derived, and show how the asymptotically AdS4 electrically charged Kerr-Newman black hole in 4d $$ \mathcal{N} $$ N = 2 supergravity is embedded in the classification. In addition, we present the conditions for the near-horizon geometry of rotating black strings in Type IIB by using dualities with the 11d setup.

We present a novel way to classify Calabi-Yau threefolds by systematically studying their infinite volume limits. Each such limit is at infinite distance in Kähler moduli space and can be classified by an associated limiting mixed Hodge structure. We then argue that the such structures are labeled by a finite number of degeneration types that combine into a characteristic degeneration pattern associated to the underlying Calabi-Yau threefold. These patterns provide a new invariant way to present crucial information encoded in the intersection numbers of Calabi-Yau threefolds. For each pattern, we also introduce a Hasse diagram with vertices representing each, possibly multi-parameter, decompactification limit and explain how to read off properties of the Calabi-Yau manifold from this graphical representation. In particular, we show how it can be used to count elliptic, K3, and nested fibrations and determine relations of elliptic fibrations under birational equivalence. We exemplify this for hypersurfaces in toric ambient spaces as well as for complete intersections in products of projective spaces.