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

A twistor string for the ABJ(M) theory