Type IIA AdS4 compactifications on cosets, interpolations and domain walls

TL;DR

<3-5 sentence high-level summary> This work classifies a broad class of type IIA flux vacua with N=1 supersymmetry compactified to AdS4 on six-dimensional coset spaces with left-invariant SU(3)-structures, showing that, in the absence of localized sources, the internal torsion is confined to $\mathcal{W}^-_1$ and $\mathcal{W}^-_2$ and that each coset has a nearly-Kähler point (i.e., they are deformations of nearly-Kähler manifolds). Through a detailed case-by-case analysis of six cosets, the authors derive explicit left-invariant SU(3)-structures, compute the torsion data, and specify fluxes, identifying four cosets that realize AdS4 vacua without sources and characterizing when $\mathcal{W}^-_2$ can be nonzero. They also present a simple radial ansatz that yields smooth domain-wall interpolations between AdS4 vacua of different radii and discuss Hitchin flow to seven dimensions, connecting to G2-holonomy cones over nearly-Kähler M6. The results provide a concrete atlas of AdS4 flux vacua on cosets, clarify coset equivalences, and offer a framework for constructing 4D effective theories and brane configurations arising from these compactifications.

Abstract

We present a classification of a large class of type IIA N=1 supersymmetric compactifications to AdS4, based on left-invariant SU(3)-structures on coset spaces. In the absence of sources the parameter spaces of all cosets leading to a solution contain regions corresponding to nearly-Kaehler structure. I.e. all these cosets can be viewed as deformations of nearly-Kaehler manifolds. Allowing for (smeared) six-brane/orientifold sources we obtain more possibilities. In the second part of the paper, we use a simple ansatz, which can be applied to all six-dimensional coset manifolds considered here, to construct explicit thick domain wall solutions separating two AdS4 vacua of different radii. We also consider smooth interpolations between AdS4 x M6 and R^{1,2} x M7, where M6 is a nearly-Kaehler manifold and M7 is the G2-holonomy cone over M6.

Figures (4)

• Figure 1: The coset space $\frac{\text{Sp(2)}}{\text{S}(\text{U(2)}\times \text{U(1)})}$ fibered over its two-dimensional moduli space $\mathfrak{M}$. The nearly-Kähler limit corresponds to the line $a=c$ in $\mathfrak{M}$, see section 4.3 below. In the full quantum theory the moduli can only assume discrete values.
• Figure 2: A domain wall in four noncompact dimensions $\mathcal{M}_4$ separating a region of AdS$_4$ from a region of $\mathbb{R}^{1,3}$. The internal manifold $\mathcal{M}_6$ is fibered over $\mathcal{M}_4$. Far from the wall $\mathcal{M}_6$ should be independent of $r$, the distance from the wall.
• Figure 3: A singular interpolating solution. The internal six-dimensional manifold $\mathcal{M}_6$ is fibered over the radial $r$-dimension, forming a seven-dimensional manifold $\mathcal{M}_7$ whose $r$=constant slices are diffeomorphic to $\mathcal{M}_6$. At $r=r_{\star}$ the six-dimensional fiber shrinks to zero size.
• Figure 4: A domain wall solution separating two AdS$_4$ vacua of different radii. The internal six-dimensional manifold $\mathcal{M}_6$ is fibered over the radial $r$-dimension, forming a seven-dimensional manifold $\mathcal{M}_7$ whose $r$=constant slices are diffeomorphic to $\mathcal{M}_6$. As $r\rightarrow \pm\infty$ the external four-dimensional space asymptotes to AdS$_4$.