Abstract
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 as 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 (DFT) 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 ${\mathbb T}^6/{\mathbb Z}_4$.
Highlights
Type II supergravity theories admit generalized fluxes via a successive application of T-duality on the three-form H3 which results in a chain of geometric and nongeometric fluxes given as follows [1,2,3,4,5,6,7]: Hijk → ωijk → Qijk → Rijk: ð1:1ÞGenerically, such fluxes can appear as parameters in the four-dimensional (4D) effective potential, and subsequently can help in developing a suitable scalar potential which could be useful for various model building purposes
(ii) We implement the robust N 1⁄4 2 results of double field theory (DFT) reduction on Calabi-Yau threefolds [47] to provide an alternate derivation of our symplectic formulation ensuring that there is a higher dimensional theory which upon dimensional reduction results in the same nongeometric type IIA scalar potential derived from a generalized flux superpotential
III, we present a set of peculiar flux combinations which we subsequently use for presenting a symplectic formulation of the scalar potential, and its dimensional oxidation
Summary
Type II supergravity theories admit generalized fluxes via a successive application of T-duality on the three-form H3 which results in a chain of geometric and nongeometric fluxes given as follows [1,2,3,4,5,6,7]: Hijk → ωijk → Qijk → Rijk: ð1:1Þ. A very robust analysis has been performed by considering the DFT reduction on generic Calabi-Yau threefold, and subsequently the generic N 1⁄4 2 results have been used to derive the N 1⁄4 1 type IIB effective potential with nongeometric fluxes [47] In all these studies it has been found that the F-term and D-term contributions of the 4D effective scalar potential combines in a specific way such that they correspond to some kinetic pieces of a ten-dimensional action
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