| Summary: | We consider maximal gauged supergravity in 4D with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ISO</mi><mo>(</mo><mn>7</mn><mo>)</mo></mrow></semantics></math></inline-formula> gauge group, which arises from a consistent truncation of massive IIA supergravity on a six-sphere. Within its G<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>-invariant sector, the theory is known to possess a supersymmetric AdS extremum, as well as two non-supersymmetric ones. In this context, we provide a first-order formulation of the theory by making use of the Hamilton–Jacobi (HJ) formalism. This allows us to derive a positive energy theorem for both non-supersymmetric extrema. Subsequently, we also find novel non-supersymmetric domain walls (DWs) interpolating between the supersymmetric extremum and each of the other two. Finally, we discuss a perturbative HJ technique that may be used in order to solve for curved DW geometries.
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