Minimal $D=4$ truncations of type IIA

Understand

Consistent embeddings are found of the minimal $\mathcal{N} = 2$ and $\mathcal{N} = 3$ gauged supergravities in four dimensions into its maximally supersymmetric, $\mathcal{N} = 8$, counterpart with a dyonic ISO(7) gauging.

• These minimal truncations retain the metric along with relevant U(1) and SO(3) R-symmetry gauge fields selected from the ISO(7) ones.
• The remaining ISO(7) gauge fields are turned off, with subtleties introduced by the dyonic gauging, and the scalars are fixed to their expectation values at the $\mathcal{N} = 2$ and $\mathcal{N} = 3$ vacua of the $\mathcal{N} = 8$ theory.
• Using the truncation formulae for massive type IIA supergravity on the six-sphere to $D=4$ $\mathcal{N} = 8$ ISO(7) supergravity, the minimal $D=4$ $\mathcal{N} = 2$ and $\mathcal{N} = 3$ gauged supergravities are then uplifted consistently to ten dimensions.