TL;DR
This paper investigates the construction of three-dimensional superconformal gauge theories with Chern-Simons terms, identifying classes with N=1 and N=2 supersymmetry and demonstrating the non-existence of N=8 theories.
Contribution
It provides a systematic analysis of possible Lagrangian formulations for superconformal Chern-Simons theories with various supersymmetries, highlighting the limitations for N=8.
Findings
N=1 and N=2 superconformal Chern-Simons theories are constructible.
No interacting N=8 superconformal Chern-Simons theories exist.
The study clarifies the landscape of supersymmetric gauge theories in three dimensions.
Abstract
We explore the possibilities for constructing Lagrangian descriptions of three-dimensional superconformal classical gauge theories that contain a Chern-Simons term, but no kinetic term, for the gauge fields. Classes of such theories with N = 1 and N = 2 supersymmetry are found. However, interacting theories of this type with N = 8 supersymmetry do not exist.
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