Embedding the SU(3) sector of SO(8) supergravity in D=11

The SU(3)-invariant sector of maximal supergravity in four dimensions with an SO(8) gauging is uplifted to D = 11 supergravity. In order to do this, the SU(3)-neutral sector of the tensor and duality hierarchies of the D = 4 N = 8 supergravity is first worked out. The consistent D = 11 embedding of the full, dynamical SU(3) sector is then expressed at the level of the D = 11 metric and three-form gauge field in terms of these D = 4 tensors. The redundancies introduced by this approach are eliminated at the level of the D = 11 four-form field strength by making use of the D = 4 duality hierarchy. Our results encompass previously known truncations of D = 11 supergravity down to sectors of SO(8) supergravity with symmetry larger than SU(3), and include new ones. In particular, we obtain a new consistent truncation of D = 11 supergravity to minimal D = 4 H = 2 gauged supergravity.