The maximal D=5 supergravities

The general Lagrangian for maximal supergravity in five spacetime dimensions is presented with vector potentials in the 27¯ and tensor fields in the 27 representation of E6(6). This novel tensor-vector system is subject to an intricate set of gauge transformations, describing 3(27−t) massless helicity degrees of freedom for the vector fields and 3t massive spin degrees of freedom for the tensor fields, where the (even) value of t depends on the gauging. The kinetic term of the tensor fields is accompanied by a unique Chern-Simons coupling which involves both vector and tensor fields. The Lagrangians are completely encoded in terms of the embedding tensor which defines the E6(6) subgroup that is gauged by the vectors. The embedding tensor is subject to two constraints which ensure the consistency of the combined vector-tensor gauge transformations and the supersymmetry of the full Lagrangian. This new formulation encompasses all possible gaugings.