Taxonomy of scalar potential with U-dual fluxes

Abstract

In the context of $N=1$ four-dimensional type IIB supergravity theories, the U-dual completion arguments suggest to include four S-dual pairs of fluxes in the holomorphic superpotential, namely the so-called $(F,H),(Q,P),(P^{\prime },Q^{\prime })$ and $(H^{\prime },F^{\prime })$. These can generically induce cubic polynomials for the complex-structure moduli as well as the Kähler-moduli in the flux superpotential. In this article, we explore the insights of the four-dimensional non-geometric scalar potential in the presence of such generalized U-dual fluxes by considering an explicit type IIB toroidal compactification model based on an orientifold of ${\mathbb{T}}^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ orbifold. First, we observe that the flux superpotential induces a huge scalar potential having a total of 76276 terms involving 128 flux parameters and 14 real scalars. Subsequently, we invoke a new set of (the so-called) ``axionic fluxes" comprising combinations of the standard fluxes and the RR axions, and it turns out that these axionic fluxes can be very useful in rewriting the scalar potential in a relatively compact form. In this regard, using the metric of the compactifying toroidal sixfold, we present a new formulation of the effective scalar potential, which might be useful for understanding the higher-dimensional origin of the various pieces via the so-called ``dimensional oxidation" process. We also discuss the generalized Bianchi identities and the tadpole cancellation conditions, which can be important while seeking the physical (AdS/dS) vacua in such models.

v3: 48 pages, To appear in Physical Review D

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Cited by in corpus (4)

• On the limitations of non-geometric fluxes to realize dS vacua
• Symplectic formulation of the type IIB scalar potential with U-dual fluxes
• Reading-off the non-geometric scalar potentials with U-dual fluxes
• Systematic exploration of the non-geometric flux landscape