N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds

TL;DR

This paper constructs and analyzes new superconformal Chern-Simons theories with enhanced supersymmetry, connecting them to M2-branes on orbifolds and extending known models like ABJM.

Contribution

It explicitly constructs $ ext{N}=5$ and 6 superconformal theories with specific gauge groups, linking them to orbifold geometries and orientifold projections of ABJM.

Findings

Constructed $ ext{N}=5$, $Sp(2M) imes O(N)$ theories.

Identified $ ext{N}=6$, $Sp(2M) imes O(2)$ theories.

Connected $ ext{N}=5$ theories to orientifolds of ABJM.

Abstract

We explore further our recent generalization of the $\mathcal{N}=4$ superconformal Chern-Simons theories of Gaiotto and Witten. We find and construct explicitly theories of enhanced $\mathcal{N}=5$ or 6 supersymmetry, especially $\mathcal{N}=5$, $Sp(2M)\times O(N)$ and $\mathcal{N}=6$, $Sp(2M)\times O(2)$ theories. The $U(M)\times U(N)$ theory coincides with the $\mathcal{N}=6$ theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We argue that the $\mathcal{N}=5$ theory with $Sp(2N)\times O(2N)$ gauge group can be understood as an orientifolding of the ABJM model with $U(2N)\times U(2N)$ gauge group. We briefly discuss the Type IIB brane construction of the $\mathcal{N}=5$ theory and the geometry of the M-theory orbifold.