Halving ISO(7) supergravity

Half-maximal, A1 = 4, sectors of D = 4 A1 = 8 supergravity with a dyonic ISO(7) gauging are investigated. We focus on a half-maximal sector including three vector multiplets, that arises as a certain SO(3)R-invariant sector of the full theory. We discuss the embedding of this sector into the largest half-maximal sector of the A1 = 8 supergravity retaining six vector multiplets. We also provide its canonical A1 = 4 formulation and show that, from this perspective, our model leads in its own right to a new explicit gauging of A1 = 4 supergravity. Finally, expressions for the restricted duality hierarchy are given and the vacuum structure is investigated. Five new non-supersymmetric AdS vacua are found numerically. The previously known A1 = 2 and A1 = 3 AdS vacua are also contained in our A1 = 4 model. Unlike when embedded in previously considered sectors with fewer fields, these vacua exhibit their full A1 = 2 and A1 = 3 supersymmetry within our A1 = 4 model.