Orbifolding the Membrane Action

TL;DR

This paper analyzes a class of ${\mathbb Z}_n$ orbifolds of the ABJM theory to generate ${\cal N}=4$ membrane theories and computes their moduli spaces. By enforcing a quantization condition $k=k'n$, the authors show that, in several orbifold patterns, the moduli spaces align with membranes probing $C^4/(Z_k \times Z_n)$. They classify SUSY preservation across orbifolds, derive explicit moduli-space structures from D- and F-term equations, and discuss constraints for coprimality of $k'$ and $n$. The results support the geometric interpretation of these orbifolds, with caveats for certain even/odd cases and non-coprime parameters, suggesting avenues for extending to non-Abelian orbifolds.

Abstract

We study a simple class of orbifolds of the N=6 Chern-Simons Matter theory proposed by Aharony, Bergman, Jafferis and Maldacena. They are considered as a world volume theory of membranes probing C^4/ (Z_k x Z_n) and include a new membrane theory with N=4 supersymmetries. We find that the moduli spaces of them are consistent with the fact that they probe C^4/ (Z_k x Z_n).

Figures (3)

• Figure 1: Quiver diagram I
• Figure 2: Quiver diagram II
• Figure 3: Quiver diagram III