Supersymmetric Flux Compactifications and Calabi-Yau Modularity

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 ${\mathbb{P}}^4(1,1,2,2,2)$.

v2: References added; examples added and removed. 20 pages + appendices, 7 tables