Charting the landscape of N=4 flux compactifications

TL;DR

This work develops a comprehensive framework to classify vacua of isotropic ${\mathcal N}=4$ flux compactifications by unifying the embedding-tensor formulation of half-maximal supergravity with algebraic-geometry techniques. By reducing to an ${\rm SO}(3)$-invariant STU sector and exploiting a flux–embedding-tensor dictionary, the authors systematically locate all critical points of the scalar potential for geometric IIA and non-geometric IIB backgrounds, computing full mass spectra and SUSY properties. They find a unique geometric IIA theory with four $AdS_{4}$ vacua (one SUSY, others non-SUSY but perturbatively stable) and no $dS_{4}$ in this sector, alongside a novel $dS_{4}$ solution arising from a non-semisimple gauging; in IIB, non-geometric fluxes yield additional vacua, including a fully ${\cal N}=4$ AdS$_4$ background and a non-semisimple de Sitter solution. Overall, the paper maps moduli stabilization and stability in half-maximal supergravity to explicit string backgrounds, revealing a richer landscape in non-geometric settings and establishing connections between ${\cal N}=4$ gaugings and ${\cal N}=1$ effective theories.

Abstract

We analyse the vacuum structure of isotropic Z_2 x Z_2 flux compactifications, allowing for a single set of sources. Combining algebraic geometry with supergravity techniques, we are able to classify all vacua for both type IIA and IIB backgrounds with arbitrary gauge and geometric fluxes. Surprisingly, geometric IIA compactifications lead to a unique theory with four different vacua. In this case we also perform the general analysis allowing for sources compatible with minimal supersymmetry. Moreover, some relevant examples of type IIB non-geometric compactifications are studied. The computation of the full N=4 mass spectrum reveals the presence of a number of non-supersymmetric and nevertheless stable AdS_4 vacua. In addition we find a novel dS_4 solution based on a non-semisimple gauging.

Figures (2)

• Figure 1: $\mathbb{T}^{6} = \mathbb{T}^{2}_{1} \times \mathbb{T}_{2}^{2} \times \mathbb{T}_{3}^{2}$ torus factorisation and the coordinate basis.
• Figure 2: Sketch of the correspondence between the field picture (crossed dots) and the flux picture (filled dots). The left diagram represents moduli space, whereas the right diagram illustrates the space of fluxes.