Analytic Periods via Twisted Symmetric Squares

Abstract

We study the symmetric square of Picard-Fuchs operators of genus one curves and the thereby induced generalized Clausen identities. This allows the computation of analytic expressions for the periods of all one-parameter K3 manifolds in terms of elliptic integrals. The resulting expressions are globally valid throughout the moduli space and allow the explicit inversion of the mirror map and the exact computation of distances, useful for checks of the Swampland Distance Conjecture. We comment on the generalization to multi-parameter models and provide a two-parameter example.

36 pages, 1 figure; v2: references added, typos corrected, matches published version

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• Heterotic de Sitter Beyond Modular Symmetry
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• 4d strings at strong coupling
• Mass Hierarchies and Quantum Gravity Constraints in DKMM-refined KKLT
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme