A twistor string for the ABJ(M) theory

We construct an open string theory whose single-trace part of the tree-level S-matrix reproduces the S-matrix of the ABJ(M) theory with a unitary gauge group. We also demonstrate that the multi-trace part of the string theory tree-level S-matrix {which has no counterpart in the pure N = 6 super-Chern-Simons theory {is due to conformal supergravity interactions and identify certain Lagrangian interaction terms. Our construction suggests that there exists a higher dimensional theory which can be dimensionally-reduced, in a certain sense, to the ABJ(M) theory. It also suggests a generalization of this theory to product gauge groups with more than two factors.