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We propose three-dimensional N=6 superconformal U(N) X U(M) and SU(N) X SU(N)Chern-Simons gauge theories with two pairs of bifundamental chiral superfieldsin the (N, M) and (\overline{N}, \overline{M}) representations and in the (N,N) and (\overline{N}, \overline{N}) representations, respectively. We alsopropose the superconformal U(1) X U(1) gauge theories that have n pairs ofbifundamental chiral superfields with U(1) X U(1) charges (\pm 1, \mp 1) or(\pm 1, \pm 1). Although these U(1) X U(1) gauge theories have global symmetrySU(2n), the R-symmetry is SO(6) for n=2, and might be SO(2n) or SO(2n+1) for 3\leq n \leq 8. In addition, we show that from either the generalized ABJMtheories, or our U(N) X U(M) theories, or the N=5 superconformal O(N) X USp(2M)gauge theories, we can derive all the N \geq 5 superconformal Chern-Simonsgauge theories except the N=5 superconformal G_2 X USp(2) gauge theory and ourU(1) X U(1) gauge theories with n \not= 2 and 4. Furthermore, we derive thethree-dimensional N=8 superconformal U(1) X U(1) gauge theory from the BLGtheory, and study the corresponding moduli space. With the novel Higgsmechanism in the unitary gauge, we suggest that it describes a D2-brane and adecoupled D2-brane.

Three-Dimensional N \geq 5 Superconformal Chern-Simons Gauge Theories And Their Relations