Reading-off the non-geometric scalar potentials with U-dual fluxes

TL;DR

This paper introduces compact master formulae for scalar potentials in type IIB superstring compactifications with U-dual fluxes, simplifying the analysis of complex flux-induced potentials and aiding in exploring non-geometric flux vacua.

Contribution

It provides a set of generic formulae that allow reading off scalar potentials directly from topological data, reducing complexity in studying flux vacua.

Findings

Simplified scalar potential expressions for explicit models

Reduced terms from over 76,000 to a few thousand in examples

Demonstrated applicability to multiple Calabi-Yau models

Abstract

In the context of four-dimensional ${\cal N} = 1$ type IIB superstring compactifications, the U-dual completion of the holomorphic flux superpotential leads to four S-dual pairs of fluxes, namely $(F, H), (Q, P), (P', Q')$ and $(H', F')$. It has been observed that the scalar potentials induced by such generalized superpotentials typically have an enormous amount of terms, making it hard to study any phenomenological aspects such as moduli stabilization. In this regard, we present a set of generic master formulae which not only formulate the scalar potential in a compact way but also enable one to {\it read-off} the various scalar potential pieces by simply knowing a set of topological data of the compactifying Calabi Yau and its mirror threefold. We demonstrate the applicability of our master formulae by {\it reading-off} the scalar potentials for five explicit models, and using a set of {\it axionic flux} combinations we show that 76276 terms arising from the flux superpotential in a ${\mathbb T}^6/({\mathbb Z}_2\times{\mathbb Z}_2)$-based model can be equivalently expressed by using 2816 terms, while 11212 terms arising from the flux superpotential in a Quintic-based model can be equivalently expressed by 668 terms! We argue that the master formulae presented in this work can be useful in an analytic exploration of the rich landscape of the non-geometric flux vacua.