Supersymmetric Flux Compactifications and Calabi-Yau Modularity

Published 16 Jan 2020 in hep-th, math.AG, and math.NT | (2001.06022v2)

Abstract: Flux compactification of IIB string theory associates special points in Calabi-Yau moduli space to choices of (pairs of) integral three-form fluxes. In this paper, we propose that supersymmetric flux vacua are modular. That is, to a supersymmetric flux vacuum arising in a variety defined over $\mathbb{Q}$, we associate a two-dimensional Galois representation that we conjecture to be modular. We provide numerical evidence for our conjecture by examining flux vacua arising on the octic hypersurface in $\mathbb{P}^{{4}(1,1,2,2,2)$.}