The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets

TL;DR

The paper constructs and analyzes a broad set of N=1 type IIA AdS$_4$ vacua on nilmanifolds and coset spaces, employing explicit left-invariant SU(3)-structure data to derive the 4D effective supergravity action and to compute the light moduli spectrum. It cross-checks 4D results with direct Kaluza-Klein reductions (notably on $T^6$ and the Iwasawa manifold), finds complete agreement in those cases, and shows that all coset models stabilize all moduli at tree level except for ${ m SU(2) imes SU(2)}$ in the nilmanifold-coset family. The analysis reveals that most coset models admit negative curvature regions, which can potentially bypass inflation no-go theorems, and discusses the prospects for decoupling Kaluza-Klein modes, uplift to de Sitter, and constructing phenomenologically viable brane sectors. Overall, the work provides a concrete, consistent framework for evaluating moduli stabilization, mass spectra, and inflationary viability in flux compactifications with geometric fluxes.

Abstract

We consider string theory compactifications of the form AdS4 x M6 with orientifold six-planes, where M6 is a six-dimensional compact space that is either a nilmanifold or a coset. For all known solutions of this type we obtain the four-dimensional N=1 low energy effective theory by computing the superpotential, the Kaehler potential and the mass spectrum for the light moduli. For the nilmanifold examples we perform a cross-check on the result for the mass spectrum by calculating it alternatively from a direct Kaluza-Klein reduction and find perfect agreement. We show that in all but one of the coset models all moduli are stabilized at the classical level. As an application we show that all but one of the coset models can potentially be used to bypass a recent no-go theorem against inflation in type IIA theory.

Figures (7)

• Figure 1: Mass spectrum of $\frac{\text{G}_2}{\text{SU(3)}}$.
• Figure 2: Mass spectrum of $\frac{\text{Sp(2)}}{\text{S}(\text{U(2)}\times \text{U(1)})}$.
• Figure 3: Mass spectrum of the continuation of $\frac{\text{Sp(2)}}{\text{S}(\text{U(2)}\times \text{U(1)})}$ to negative $\sigma$.
• Figure 4: Mass spectrum of $\frac{\text{SU(3)}}{\text{U(1)}\times \text{U(1)}}$.
• Figure 5: Mass spectrum of $\frac{\text{SU(3)}}{\text{U(1)}\times \text{U(1)}}$ for negative $\sigma$ and $\rho$.