Relating U(N) × U(N) to SU(N) × SU(N) Chern-Simons membrane theories

Abstract

By integrating out the U(1)_B gauge field, we show that the U(n) × U(n) ABJM theory at level k is equivalent to a identification of the Chern-Simons theory, but only when n and k are coprime. As a consequence, the k = 1 ABJM model for two M2-branes in can be identified with the theory. We also conjecture that the U(2) × U(2) ABJM model at k = 2 is equivalent to the -theory.