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Supersymmetric gauge theories in three dimensions

We show how superconformal gaugings in three dimensions can be systematically constructed using the embedding tensor technique. These gaugings have been argued to describe the worldvolume theory of multiple M2‐branes. Applying our technique we construct the most general superconformal gaugings with 𝒩 = 5, 6 and 8 supersymmetry. In the case of 𝒩 = 5 supersymmetry we find three exceptional gaugings. We briefly discuss new developments concerning the massive deformations of the superconformal gauge theories.