Three-Dimensional N ≥ 5 Superconformal Chern-Simons Gauge Theories And Their Relations
Abstract
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 superfields in the (N, M) and (N, M) representations and in the (N, N) and (N, N) representations, respectively. We also propose the superconformal U(1) X U(1) gauge theories that have n pairs of bifundamental chiral superfields with U(1) X U(1) charges ( 1, 1) or ( 1, 1). Although these U(1) X U(1) gauge theories have global symmetry SU(2n), the R-symmetry is SO(6) for n=2, and might be SO(2n) or SO(2n+1) for 3 ≤ n ≤ 8. In addition, we show that from either the generalized ABJM theories, 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 ≥ 5 superconformal Chern-Simons gauge theories except the N=5 superconformal G2 X USp(2) gauge theory and our U(1) X U(1) gauge theories with n = 2 and 4. Furthermore, we derive the three-dimensional N=8 superconformal U(1) X U(1) gauge theory from the BLG theory, and study the corresponding moduli space. With the novel Higgs mechanism in the unitary gauge, we suggest that it describes a D2-brane and a decoupled D2-brane.