Tri-Sasakian consistent reduction

We establish a universal consistent Kaluza-Klein truncation of M-theory based on seven-dimensional tri-Sasakian structure. The four-dimensional truncated theory is an N = 4 gauged supergravity with three vector multiplets and a non-abelian gauge group, containing the compact factor SO(3). Consistency follows from the fact that our truncation takes exactly the same form as a left-invariant reduction on a specific coset manifold, and we show that the same holds for the various universal consistent truncations recently put forward in the literature. We describe how the global symmetry group SL(2, R) x SO(6, 3) is embedded in the symmetry group E-7(7) of maximally supersymmetric reductions, and make the connection with the approach of Exceptional Generalized Geometry. Vacuum AdS(4) solutions spontaneously break the amount of supersymmetry from N = 4 to N = 3, 1 or 0, and the spectrum contains massive modes. We find a subtruncation to minimal N = 3 gauged supergravity as well as an N = 1 subtruncation to the SO(3)-invariant sector. We also show that a reduction on the homogeneous space N-010 enhances the universal tri-Sasakian truncation with a Betti vector multiplet.