We study the four-dimensional (4D) scalar potential arising from a generalized type IIA flux superpotential including the (non)geometric fluxes. First, we show that using a set of peculiar flux combinations, the 4D scalar potential can be formulated into a very compact form. This is what we call the “symplectic formulation” from which one could easily anticipate the ten-dimensional origin of the effective scalar potential. We support our formulation through an alternate derivation of the scalar potential via considering the double field theory reduction on a generic Calabi-Yau orientifold. In addition, we also exemplify the insights of our formulation with explicit computations for two concrete toroidal examples using orientifolds of the complex threefolds ${\mathbb{T}}^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ and ${\mathbb{T}}^6/{\mathbb{Z}}_4$.

• Received 2 May 2018

DOI:https://doi.org/10.1103/PhysRevD.98.046009

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Published by the American Physical Society