A bstract Geometric modularity has recently been conjectured to be a characteristic feature of flux vacua with W = 0. This paper provides support for the conjecture by computing motivic modular forms in a direct way for several string compactifications for which such vacua are known to exist. The analysis of some Calabi-Yau manifolds which do not admit supersymmetric flux vacua shows that the reverse of the conjecture does not hold.
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Rolf Schimmrigk (2020) studied this question.