Quiver Chern–Simons theories and 3-algebra orbifolds

We attempt to derive quiver Chern–Simons-matter theories from the Bagger–Lambert theory with Nambu bracket, through an orbifold prescription which effectively induces a dimensional reduction of the internal space for 3-algebra. We consider M2-branes on an N=4N=4 orbifold C2/Zk×C2C2/Zk×C2, and compare the result with the so-called dual Aharony–Bergman–Jafferis–Maldacena model, proposed recently by Hanany, Vegh, and Zaffaroni. Unlike the N=6N=6 example C4/ZkC4/Zk, we find ambiguities in the matrix regularization.