The maximal D=5 supergravities

TL;DR

This work constructs a universal, $E_{6(6)}$-covariant formulation of maximal supergravity in five dimensions, where vector fields reside in $\overline{\mathbf{27}}$ and tensor fields in $\mathbf{27}$, and all possible gaugings are encoded by a spurionic embedding tensor in $\mathbf{351}$. Linear and quadratic constraints on the embedding tensor guarantee a closed gauge algebra and supersymmetry, while the $T$-tensor, obtained from the coset representative, governs mass terms and the scalar potential. The authors derive the full tensor–vector gauge structure, provide the Lagrangian and SUSY transformations, and illustrate the framework with CSO and SO(5,5)$\times$SO(1,1$)$-type gaugings, including Scherk–Schwarz reductions. This approach yields a complete, symmetry-guided classification of all maximal D=5 gaugings and establishes a bridge to gauged supergravities in other dimensions, with smooth limits to ungauged theories and clear pathways to higher-dimensional embeddings.

Abstract

The general Lagrangian for maximal supergravity in five spacetime dimensions is presented with vector potentials in the \bar{27} and tensor fields in the 27 representation of E_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 E_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.