A new N=4N=4 membrane action via orbifold

We propose a new Lagrangian describing N=4N=4 superconformal field theory in three dimensions. This theory is believed to describe interacting field theory on the worldvolume of a M2-brane on an orbifold, and is obtained as a Z2Z2-quotient of the theory proposed by Bagger and Lambert. Despite unusual Chan–Paton structures, we can take Z2Z2-orbifold by using SU(2)×SU(2)SU(2)×SU(2) bifundamental representations. We also analyze the moduli space of this theory and found three branches. With an assumption of a broken U(1)U(1) symmetry, the moduli space is consistent with that of the D2-brane in the strong coupling limit of Type IIA string theory if the gauge group is O(4)O(4). Our action has manifest Z2Z2-symmetry exchanging two R4/Z2R4/Z2's in M-theory, and this suggests a new non-perturbative duality between a O2−-brane on orbifold R4/Z2R4/Z2 and a O2−-brane with D6-branes.