Classification of discrete modular symmetries in Type IIB flux vacua

Abstract

We classify discrete modular symmetries in the effective action of Type IIB string on toroidal orientifolds with three-form fluxes, emphasizing on $T^6/{\mathbb{Z}}_2$ and $T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2^{\prime })$ orientifold backgrounds. On the three-form flux background, the modular group is spontaneously broken down to its congruence subgroup whose pattern is severely constrained by a quantization of fluxes and tadpole cancellation conditions. We explicitly demonstrate that the congruence subgroups appearing in the effective action arise on magnetized D-branes wrapping certain cycles of tori.

Comments: 22 pages, v2: published version, typos corrected