Symplectic formulation of the type IIA nongeometric scalar potential

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 T-6/(Z(2)xZ(2)) and T-6/Z(4).