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Nambu-Poisson Bracket and M-Theory Branes Coupled to Antisymmetric Fluxes

By using the recently proposed prescription arXiv:0804.3629 for obtaining the $M5$ brane action from multiple $M2$ branes action in BLG theory, we examine such transition when 11 Dimensional background antisymmetric fluxes couple to the $M2$ brane world volume. Such couplings was suggested in arXiv:0805.3427 where it was used the fact that various fields in BLG theory are valued in a Lie 3-algebra. We argue that this action and promoting it by Nambu-Poisson bracket gives the expected coupling of fluxes with $M5$ brane at least at weak coupling limit. We also study some other aspects of the action for example, the gauge invariance of the theory.