Maximal Gauged Supergravity in Three Dimensions

We construct maximally supersymmetric gauged $N=16\mathrm{}$ supergravity in three dimensions, thereby obtaining an entirely new class of anti–de Sitter supergravities. These models apparently cannot be derived from any known higher-dimensional theory and point to the existence of a new type of supergravity beyond $D=11\mathrm{}$. One of their noteworthy features is a non-Abelian generalization of the duality between scalar and vector fields in three dimensions. Among the possible gauge groups, $\mathrm{SO}\left(8\right)\times \mathrm{SO}\left(8\right)$ is distinguished as the maximal compact gauge group, but there are also more exotic possibilities such as $F_{4(-20\mathrm{})}\times G_2$.