AdS_4 compactifications of AdS_7 solutions in type II supergravity

TL;DR

The paper builds AdS$_4$ vacua in type II supergravity by twisting AdS$_7$ solutions and fibering a compact three-manifold over the twist, reducing the problem to a set of ODEs that collapse to a tractable subsystem under a natural ansatz. A universal map links the AdS$_4$ data to AdS$_7$ solutions, enabling analytic expressions and a broad class of massive and massless solutions with localized D6/O6/D8 sources, including both analytic natural compactifications and numerically controlled attractor flows. The constructions are interpreted as twisted compactifications of the 6D $(1,0)$ CFT$_6$ duals, yielding ${\cal N}=1$ CFT$_3$ sectors without flavor symmetry, and illuminating flux quantization consistency across dimensions. The work combines generalized geometry, pure spinor techniques, and careful flux/topology analysis to produce a rich landscape of AdS$_4$ vacua with potential holographic applications and insights into scale separation and brane backreaction.

Abstract

We find new classes of AdS_4 solutions with localized branes and orientifolds, both analytic and numerical. We start with an Ansatz for the pure spinors inspired by a recently found class of AdS_7 x M_3 solutions in massive IIA; we replace the AdS_7 by AdS_4 x Sigma_3, and we fibre M_3 over Sigma_3 in a way inspired by a field theory SU(2) twist. We are able to reduce the problem to a system of five ODEs; a further Ansatz reduces them to three. Their solutions can be bijectively mapped to the AdS_7 solutions via a simple universal map. This also allows to find a simple analytic form for these solutions. They are naturally interpreted as twisted compactifications of the (1,0) CFT_6's dual to the AdS_7 solutions. The larger system of five ODEs also admits more general numerical solutions, again with localized branes; regularity is achieved via an attractor mechanism.

Figures (2)

• Figure 1: Massive attractor solutions. In \ref{['fig:reg-reg']} we see a solution with two regular poles, and $n_0 = -10$ (as usual, $F_0=\frac{n_0}{2\pi}$). We plot $f$ (orange), $e^\phi$ (green), $e^A$ (black), $g$ (purple), $x=\cos \psi$ (dashed). In \ref{['fig:D6-reg']} a solution with a stack of $n_2=10$ D6-branes at the north pole (left), and a regular point at the south pole (right); again $n_0=-10$, and $N=-\frac{1}{4\pi^2}\int H=-1$. In both cases, $R=6$, so $\Sigma_3=S^3$.
• Figure 2: Massive attractor solutions. In \ref{['fig:O6-reg']} we see a solution with an O6 at the north pole (left), and a regular point at the south pole (right). In \ref{['fig:D8']} a solution with two regular poles with a D8 stack in the middle (which is the sharp kink towards $r\sim 1$, most visible in the black and purple lines). In both cases, $R=6$, so $\Sigma_3=S^3$.