Superconformal Chern-Simons Theories

TL;DR

The paper assesses whether explicit Lagrangians for 3D superconformal gauge theories with a Chern-Simons term (and no gauge kinetic term) can exist, and constructs robust ${\rm obreakspace}\mathcal{N}=1$ and ${\rm obreakspace}\mathcal{N}=2$ models by coupling CS to matter with off-shell SUSY while maintaining scale invariance. It shows these theories exist and are well-defined at the classical level, but finds strong evidence that no interacting ${\rm obreakspace}\mathcal{N}=8$ theory can be realized within this setup, due in part to constraints on superpotentials and R-symmetry enhancement. The work discusses implications for the AdS/CFT dual of M-theory on $AdS_4\times S^7$ and speculates about connections to Romans massive IIA backgrounds, highlighting that a classical Lagrangian for the maximal case may be unattainable. Overall, the paper provides explicit ${\rm obreakspace}\mathcal{N}=1,2$ CS-matter frameworks and delineates obstructions to ${\rm obreakspace}\mathcal{N}=8$ in this approach, clarifying the landscape of 3D superconformal CS theories.

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.