Fluxes and gaugings: N = 1 effective superpotentials

TL;DR

The paper develops a dictionary between $N=1$ effective supergravity from flux compactifications and $N=4$ gauged supergravities, focusing on type IIA orientifolds with D6 branes on $T^6/(Z_2\times Z_2)$. It shows how fluxes $(F_p,H_3,\omega_3)$ map to gauging data, producing a concrete $N=1$ superpotential $W$ and Kähler potential $K$ for seven moduli $(S,T_A,U_A)$, and provides explicit single-flux and multi-flux examples. A major result is the construction of scenarios that stabilize all moduli in AdS$_4$, notably under a Jacobi constraint, illustrating that fully stabilized flux vacua are achievable in IIA but not generically in heterotic or certain IIB setups. The work reinforces the efficacy of gauged supergravity as a bottom-up tool to explore flux vacua and moduli stabilization, aligning low-energy effective theories with the underlying higher-dimensional constraints when brane/orientifold effects are included.

Abstract

We illustrate the correspondence between the N=1 superstring compactifications with fluxes, the N=4 gauged supergravities and the superpotential and Kähler potential of the effective N=1 supergravity in four dimensions. In particular we derive, in the presence of general fluxes, the effective N=1 supergravity theory associated to the type IIA orientifolds with D6 branes, compactified on $T^6/(Z_2 \times Z_2)$. We construct explicit examples with different features: in particular, new IIA no-scale models, new models with cosmological interest and a model which admits a supersymmetric AdS$_4$ vacuum with all seven main moduli ($S, T_A, U_A,A=1,2,3$) stabilized.