Symplectic formulation of the type IIB scalar potential with U-dual fluxes

TL;DR

This paper introduces a symplectic approach to express the complex scalar potential in type IIB string theory with U-dual fluxes, simplifying calculations and applicable to various compactification models.

Contribution

It provides a compact symplectic formulation of the type IIB scalar potential with U-dual fluxes, independent of internal metric details, applicable to diverse compactifications.

Findings

Derived a concise symplectic master-formula for the scalar potential.

Applied the formulation to a specific orientifold model with 128 flux parameters.

Demonstrated the approach's applicability beyond toroidal compactifications.

Abstract

We present a symplectic formulation of the $N =1$ four-dimensional type IIB scalar potential arising from a flux superpotential which has four S-dual pairs of fluxes demanded by the U-dual completion arguments. Our symplectic formulation presents a very compact and concise way of expressing the generic scalar potential in just a few terms via using a set of symplectic identities along with the so-called "axionic-flux" combinations. We demonstrate the utility of our symplectic master-formula by considering an underlying four-dimensional type IIB supergravity model based on a ${\mathbb T}^6/({\mathbb Z}_2 \times {\mathbb Z}_2)$ orientifold, in which the scalar potential induced by the U-dual flux superpotential results in a total of 76276 terms involving 128 flux parameters. Given that our symplectic formulation does not need the information about the metric of the internal background, it is applicable to the models beyond the toroidal compactifications such as to those which use orientifolds of the Calabi-Yau threefolds.