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Abstract We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 \( \mathcal{N}=2 \) superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special Kähler geometry near those...

We initiate a comprehensive survey of axion inflation in compactifications of type IIB string theory on Calabi-Yau hypersurfaces in toric varieties. For every threefold with h 1,1 ≤ 4 in the Kreuzer-Skarke database, we compute the metric on Kähler moduli space, as well as the matrix of four-form axion charges of Euclidean D3-branes on rigid divisors. These charges encode the...

Several recent works [1-3] have claimed that the Weak Gravity Conjecture (WGC) excludes super-Planckian displacements of axion fields, and hence large-field axion inflation, in the absence of monodromy. We argue that in theories with N ≫ 1 axions, super-Planckian axion diameters \( \mathcal{D} \) are readily allowed by the WGC. We clarify the non-trivial relationship between the...

We argue that super-Planckian diameters of axion fundamental domains can arise in Calabi-Yau compactifications of string theory. In a theory with N axions θ i , the fundamental domain is a polytope defined by the periodicities of the axions, via constraints of the form − π < Q i j θ j < π. We compute the diameter of the fundamental domain in terms of the eigenvalues f 1 2 ≤ … ≤ f...

We study the statistics of the metric on Kähler moduli space in compactifications of string theory on Calabi-Yau hypersurfaces in toric varieties. We find striking hierarchies in the eigenvalues of the metric and of the Riemann curvature contribution to the Hessian matrix: both spectra display heavy tails. The curvature contribution to the Hessian is non-positive, suggesting a...