Reading off the non-geometric scalar potentials via topological data of the Calabi Yau manifolds

Understand

In the context of studying the 4D effective potentials of type IIB non-geometric flux compactifications, this article has a twofold goal.

• First, we present a modular invariant symplectic rearrangement of the tree level non-geometric scalar potential arising from a flux superpotential which includes the S-dual pairs of non-geometric fluxes $(Q, P)$, the standard NS-NS and RR three-form fluxes $(F_3, H_3)$ and the geometric flux ($\omega$).
• This `symplectic formulation' is valid for arbitrary numbers of K\"ahler moduli, and the complex structure moduli which are implicitly encoded in a set of symplectic matrices.
• In the second part, we further explicitly rewrite all the symplectic ingredients in terms of saxionic and axionic components of the complex structure moduli.