On Type IIB moduli stabilization and N = 4, 8 supergravities

TL;DR

The paper establishes a detailed map between Type IIB flux compactifications with dual fluxes and gauged ${\cal N}=4$ (and potential ${\cal N}=8$) supergravities, using Jacobi identities to constrain flux backgrounds. It shows that many flux configurations enforce proportionality between electric and magnetic gaugings, hindering full moduli stabilization, and introduces an exclusion principle based on the rank of a flux-assembly matrix to rule out large regions of the parameter space. By analyzing AdS and Minkowski vacua (including spontaneous ${\cal N}=4\to1$ breaking and Freed-Witten anomaly constraints), the work demonstrates both the potential for controlled fully stabilized vacua in carefully chosen cases (often with branes) and the general difficulty of achieving complete stabilization under the strongest symmetry constraints. The results provide a rigorous bridge between string-theoretic flux backgrounds and four-dimensional gauged supergravity, clarifying when untwisted sectors correspond to exact truncations and how branes and primed fluxes modify the landscape. Overall, the study highlights the delicate balance between flux-induced moduli potentials, duality-consistent gaugings, and brane-induced constraints in obtaining realistic, stable vacua with controllable couplings.

Abstract

We analyze D = 4 compactifications of Type IIB theory with generic, geometric and non-geometric, dual fluxes turned on. In particular, we study N = 1 toroidal orbifold compactifications that admit an embedding of the untwisted sector into gauged N = 4, 8 supergravities. Truncations, spontaneous breaking of supersymmetry and the inclusion of sources are discussed. The algebraic identities satisfied by the supergravity gaugings are used to implement the full set of consistency constraints on the background fluxes. This allows to perform a generic study of N = 1 vacua and identify large regions of the parameter space that do not admit complete moduli stabilization. Illustrative examples of AdS and Minkowski vacua are presented.

Figures (1)

• Figure 1: The rank of $\cal F$ is represented when one or two generic electric gaugings are turned on in the ${\cal N} = 4$ (upper graph) and ${\cal N}= 8$ (lower graph) constraints. Yellow points are excluded for moduli stabilization because ${\rm rank} {\cal F}= \# {\rm magnetic \ fluxes} - 1 = 23$.