We analyze the moduli space of the low-energy limit of 3-dimensional N = 3 MaxwellChern-Simons theories described by circular quiver diagrams, as for 4-dimensional elliptic models. We define the theories by using D3-NS5-(k,1)5-brane systems with an arbitrary number of fivebranes. The supersymmetry is expected to be enhanced to N =4i n the low-energy limit. We show that the Higgs branch, in which all bifundamental scalar fields develop vacuum expectation values, is an abelian orbifold of C 4 . We confirm that the same geometry is obtained as an M-theory dual of the brane system. We also consider theories realized by introducing more than two kinds of fivebranes, and obtain nontoric fourfolds as moduli spaces. Recently, there has been great interest in 3-dimensional superconformal field theories as theories for describing multiple M2-branes in various backgrounds. This was triggered by the proposal of a new class of 3-dimensional theories by Bagger and Lambert, 1)–3) and Gusstavson. 4),5) The model (BLG model) possesses N(d=3) =8 superconformal symmetry and is based on Lie 3-algebra. The action of the BLG model includes the structure constant f abc d of a Lie 3-algebra, which determines the form of the interactions, and a metric h ab , which appears in the coefficients of the kinetic terms. These tensors must satisfy certain conditions required by the supersymmetry invariance of the action. If these tensors satisfy the conditions, we can write down the action of a BLG model. The constraint imposed on the structure constant is called a fundamental identity. It was soon realized that the identity is very restrictive, 6) and it was proved that if we assume that the metric is positive definite and the algebra is finite dimensional, there is only one nontrivial Lie 3-algebra, 7),8) which is called an A4 algebra. The BLG model based on the A4 algebra is a SU(2)×SU(2) Chern-Simons theory with levels k and −k for each SU(2) factor. Analysis of this model showed that it describes a pair of M2-branes in certain orbifold backgrounds. 9)–11) As a theory for an arbitrary number of M2-branes, a model based on an algebra with a Lorenzian metric was proposed in Refs. 12)– 14). Because of the indefinite metric, the model includes unwanted ghost modes. Although the ghost modes can be removed by treating them as background fields satisfying classical equations of motion, 14),15) or by gauging certain symmetries and fixing them, 16),17) this procedure breaks the conformal invariance, and the theory becomes D2-brane theory 14),16),18) by the mechanism proposed in Ref. 19) unless the