Complete the classification of gauged maximal supergravities in three dimensions

Complete the classification of gauged maximal supergravities in D = 3 within the embedding tensor formalism, where the embedding tensor transforms in the 1 ⊕ 3875 representation of E8(8), identifying all consistent gauge groups and couplings.

Background

The embedding tensor formalism provides a unified description of all gaugings of maximal supergravities by specifying how gauge groups are embedded into the global duality groups, subject to linear and quadratic constraints. In D = 4, the embedding tensor lies in the 912 of E7(7) and yields a comprehensive classification of gaugings.

In other dimensions the formalism also works, but in D = 3 the full classification remains incomplete; there the embedding tensor resides in the 1 ⊕ 3875 of E8(8). Completing this classification is essential for a systematic understanding of all consistent gauged maximal supergravities in three dimensions.