Symplectic formulation of the type IIA nongeometric scalar potential

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 ${\mathbb{T}}^6/{\mathbb{Z}}_4$.

arXiv commentv4: 33 pages, typos fixed in eqn. (4.22) and (4.23), and some cosmetic changes in the title; version to appear in PRD

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• How many fluxes fit in an EFT?
• Dictionary for the type II nongeometric flux compactifications
• Rigid nongeometric orientifolds and the swampland
• $T$-dualizing the de-Sitter no-go scenarios
• Taxonomy of scalar potential with U-dual fluxes
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• Reading-off the non-geometric scalar potentials with U-dual fluxes
• Duality rules for more mixed-symmetry potentials
• On Formulating the Non-Geometric Scalar Potentials
• Systematic exploration of the non-geometric flux landscape