Taxonomy of scalar potential with U-dual fluxes

In the context of N =1 four-dimensional type-IIB supergravity theories, the U-dual completion arguments suggest including four S-dual pairs of fluxes in the holomorphic superpotential, namely the socomplex-structure moduli as well as the Kahler moduli in the flux superpotential. In this article, we explore the insights of the four-dimensional nongeometric 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 T6/(Z2 x Z2) orbifold. First, we observe that the flux superpotential induces a huge scalar potential having a total of 76,276 terms involving 128 flux parameters and 14 real scalars. Subsequently, we invoke a new set of (the so-called) "axionic fluxes" comprising of 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 higherdimensional 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 anti-de Sitter/de Sitter vacua in such models.