Positive Energy and Non-SUSY Flows in ISO(7) Gauged Supergravity

We consider maximal gauged supergravity in 4D with ISO(7) gauge group, which arises from a consistent truncation of massive IIA on six-sphere. Within its G$_2$ invariant sector, the theory is known to possess supersymmetric AdS extremum as well two non-supersymmetric ones. In this context we provide first order formulation by making use Hamilton-Jacobi (HJ) formalism. This allows us derive positive energy theorem for both extrema. Subsequently, also find novel domain walls (DW) interpolating between and each other two. Finally, discuss perturbative HJ technique that may be used solve curved DW geometries.