Types of quantum field thories
The (U-duality-)global gauge group of maximally supersymmetric 3d supergravity is E8 (its split real form ). Various subgroups of this may be promoted to local gauge groups (with gauge fields in gauged supergravity), which may be obtained via (fluxed) KK-compactification of 11-dimensional supergravity. However, 3d supergravity also admits a maximal gauging where all of is promoted to a local gauge group (Nicolai-Samtleben 00, Nicolai-Samtleben 01, table 1)). This maximal gauging in 3d supergravity is not obtained by reduction from standard 11-dimensional supergravity, see the remarks in (Nicolai-Samtleben 01, section 7) and see the followup (Hohm-Samtleben 13). In (de Wit-Nicolai 13, section 13) it is suggested that the seemingly missing degrees of freedom necessary to accomplish for U-duality-gauge enhancement after reduction may be sitting in a non-perturvative dual of the graviton (dual graviton).
Topological gauged supergravity in dimension three was first considered in
Bernard Julia, Application of supergravity to gravitation theories, in Unified field theories in more than 4 dimensions (V. D. Sabbata and E. Schmutzer, eds.), (Singapore), pp. 215–236, World Scientific, 1983.
N. Marcus, John Schwarz, Three-dimensional supergravity theories, Nucl. Phys. B228 (1983) 145.
The complete list of un-gauged supergravituies in 3 dimensions was given in
The maximally supersymmetric gauged 3d supergravitites (and their exceptional gaugings) are listed in
with details in
(see also at exceptional generalized geometry).
Hitoshi Nishino, Subhash Rajpoot, Topologican Gauging of N=16 Supergravity in Three-Dimensions, Phys.Rev. D67 (2003) 025009 (arXiv:hep-th/0209106)
Edi Gava, Parinya Karndumri, K. S. Narain, 3D gauged supergravity from SU(2) reduction of N=1 6D supergravity, JHEP 09 (2010) 028 (arXiv:1006.4997)