A New N=4 Membrane Action via Orbifold
Hiroyuki Fuji, Seiji Terashima, Masahito Yamazaki
TL;DR
The paper constructs a novel $\mathcal{N}=4$ three-dimensional superconformal membrane action by performing a $\mathbb{Z}_2$ orbifold of Bagger–Lambert theory in the $\mathrm{SU}(2)\times \mathrm{SU}(2)$ bifundamental setup. It demonstrates that the orbifold preserves $\mathcal{N}=4$ supersymmetry and yields a moduli space with three branches, which, under a broken $U(1)$ to a discrete subgroup, matches the Type IIA D2-brane moduli in the strong coupling limit for the gauge group $O(4)$; the action features a manifest $\mathbb{Z}_2$ symmetry exchanging two $\mathbb{R}^4/\mathbb{Z}_2$ sectors, suggesting a new non-perturbative duality. The authors further compare the M-theory and Type IIA pictures, showing consistency across branches and introducing an orientifold–orbifold duality, dubbed O-duality, between O2$^-$ with orbifold and O2$^-$ with D6-branes. They also discuss generalizations to other $\mathbb{Z}_2$ actions and propose checks via instanton moduli on $SU(2)$, highlighting the broader significance for membrane dynamics on orbifolds.
Abstract
We propose a new Lagrangian describing N=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 Z_2-quotient of the theory proposed by Bagger and Lambert. Despite unusual Chan-Paton structures, we can take Z_2-orbifold by using SU(2)\times 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) 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). Our action has manifest Z_2-symmetry exchanging two R^4/Z_2's in M-theory, and this suggests a new non-perturbative duality between a O2^{-}-brane on orbifold R^4/Z_2 and a O2^{-}-brane with D6-branes.