Superconformal Chern-Simons theories and the squashed seven sphere

We show that there are two supersymmetric completions of the three-dimensional Chern-Simons theory of level k with gauge group U(N) x U(N) coupled to four sets of massless scalars and spinors in the bi-fundamental representation, if we require Sp(2) is a subset of SU(4) global symmetry with the matter fields in the fundamental representation of SU(4). One is the N = 6 superconformal theory recently studied in hep-th/0806.1218 and another is a new theory with N = 1 superconformal symmetry. We conjecture that the N = 1 theory is dual to M theory on AdS4 x squashed S7/Zk.