AdS$_4$ solutions of massive IIA from dyonic ISO(7) supergravity

TL;DR

This work constructs AdS$_4$ solutions of massive IIA by uplifting critical points of the $D=4$ ${\cal N}=8$ dyonic ISO(7) supergravity, via a rigorously derived consistent truncation on $S^6$ to the SU(3)-invariant sector. It delivers explicit ten-dimensional embedding formulae, analyzes regularity and symmetry, and explores further truncations to G$_2$ and dilatons. The authors obtain new supersymmetric and non-supersymmetric AdS$_4$ vacua (notably ${\cal N}=1$ SU(3) and ${\cal N}=0$ SO(6)$_+$) and recover known ones, with detailed flux quantisation and free-energy calculations. Stability analyses show a BF-stable G$_2$-invariant non-SUSY solution, while several non-SUSY vacua are unstable; the flux quantisation results confirm these vacua as well-defined massive IIA backgrounds and hint at their holographic duals in Chern–Simons–matter theories.

Abstract

Explicit formulae are given for the consistent truncation of massive type IIA supergravity on the six-sphere to the SU(3)--invariant sector of $D=4$ ${\cal N}=8$ supergravity with dyonic ISO(7) gauging. These formulae are then used to construct AdS$_4$ solutions of massive type IIA via uplift on $S^6$ of the critical points of the $D=4$ supergravity with at least SU(3) symmetry. We find a new ${\cal N}=1$ solution with SU(3) symmetry, a new non-supersymmetric solution with SO(6) symmetry, and recover previously known solutions. We quantise the fluxes, calculate the gravitational free energies of the solutions and discuss the stability of the non-supersymmetric ones. Among these, a (previously known) G$_2$--invariant solution is found to be stable.