Taxonomy of scalar potential with U-dual fluxes

TL;DR

This paper analyzes a complex scalar potential in type IIB supergravity with generalized U-dual fluxes, providing a new compact formulation and insights into higher-dimensional origins, Bianchi identities, and vacuum conditions.

Contribution

It introduces a new compact formulation of the scalar potential with U-dual fluxes in a specific toroidal compactification, aiding understanding of its higher-dimensional structure.

Findings

Scalar potential has 76276 terms with 128 flux parameters.

Axionic fluxes help rewrite the potential more compactly.

Discussion of Bianchi identities and tadpole conditions for vacua.

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 K\"ahler-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.