Maximal Gauged Supergravity in Three Dimensions

We construct maximally supersymmetric gauged N  =  16 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. 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, SO(8)×SO(8) is distinguished as the maximal compact gauge group, but there are also more exotic possibilities such as F_4(-20)×G₂.