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

TL;DR

The paper broadens the landscape of three-dimensional superconformal Chern-Simons-matter theories by showing that ${\cal N}=4$ models with hypermultiplets of the same gauge representation admit automatic enhancement to ${\cal N}=5$, and, in certain representations, to ${\cal N}=6$. It provides explicit constructions: ${\cal N}=5$, $Sp(2M)\times O(N)$ and ${\cal N}=6$, $Sp(2M)\times O(2)$ theories, with the familiar ABJM ${\cal N}=6$, $U(M)\times U(N)$ theory recovered in this framework. The work also relates the ${\cal N}=5$ $Sp(2N)\times O(2N)$ theory to an orientifold of ABJM and identifies its M-theory dual as M2-branes on an orbifold ${\mathbb C}^4/\hat{D}_{k+2}$, while detailing a Type IIB brane realization and the corresponding M-theory geometry. Together, these results map a network linking Lie superalgebras, orientifolds, and M2-brane geometries, with implications for AdS/CFT duals and moduli-space structures of enhanced-supersymmetry theories.

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.