On Flux Vacua and Modularity

Abstract

Geometric modularity has recently been conjectured to be a characteristic feature for 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 mani-folds which do not admit supersymmetric flux vacua shows that the reverse of the conjecture does not hold.