Superpotentials for superconformal Chern-Simons theories from representation theory

Understand

These notes provide a detailed account of the universal structure of superpotentials defining a large class of superconformal Chern-Simons theories with matter, many of which appear as the low-energy descriptions of multiple M2-brane configurations.

• The amount of superconformal symmetry in the Chern-Simons-matter theory determines the minimum amount of global symmetry that the associated quartic superpotential must realise, which in turn restricts the matter superfield representations.
• Our analysis clarifies the necessary representation-theoretic data which guarantees a particular amount of superconformal symmetry.
• Thereby we shall recover all the examples of M2-brane effective field theories that have appeared in the recent literature.