M2-branes coupled to antisymmetric fluxes

By turning on antisymmetric background fluxes, we study how multiple M2-branes are coupled to them. Our investigation concentrates on the gauge invariance conditions for the Myers-Chern-Simons action. Furthermore, the dimensional reduction of M2-branes to D2-branes introduces more constraints on the newly introduced tensors. Particularly, for the theory based on A4 algebra, we are able to fix all components of them up to an overall normalization constant. These results can not be simply obtained from the previously proposed cubic matrix representation for this algebra. We also comment on cubic matrices as the representations of 3-algebras.