N = 5, 6 superconformal Chern-Simons theories and M2-branes on orbifolds

We explore further our recent generalization of the N = 4 superconformal Chern-Simons theories of Gaiotto and Witten. We find and construct explicitly theories of enhanced N = 5 or 6 supersymmetry, especially N = 5, Sp(2M) x O(N) and N = 6, Sp(2M) x O(2) theories. The U(M) x U(N) theory coincides with the N = 6 theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We argue that the N = 5 theory with Sp(2N) x O(2N) gauge group can be understood as an orientifolding of the ABJM model with U(2N) x U(2N) gauge group. We briefly discuss the Type IIB brane construction of the N = 5 theory and the geometry of the M-theory orbifold.