Symplectic formulation of the type IIA nongeometric scalar potential

TL;DR

This paper introduces a symplectic formulation of the 4D scalar potential in type IIA string theory with fluxes, simplifying its structure and linking it to ten-dimensional origins, supported by DFT reduction and explicit examples.

Contribution

It presents a novel symplectic formulation of the scalar potential that unifies various flux contributions and clarifies its ten-dimensional origin, supported by DFT analysis and explicit toroidal examples.

Findings

Compact symplectic form of the scalar potential derived.

Connection established between 4D potential and 10D origin.

Explicit computations on toroidal orientifolds demonstrate the formulation.

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