  We consider periodic arrays of M2-branes in the ABJM model in the spirit of a
circle compactification to D2-branes in type IIA string theory. The result is a
curious formulation of three-dimensional maximally supersymmetric Yang-Mills
theory in terms of fermions, seven transverse scalars, a non-dynamical gauge
field and an additional scalar `dual gluon'. Upon further T-duality on a
transverse torus we obtain a non-manifest-Lorentz-invariant description of
five-dimensional maximally supersymmetric Yang-Mills. Here the additional
scalar field can be thought of as the components of a two-form along the torus.
This action can be viewed as an M-theory description of M5-branes on ${\mathbb
T}^3$.
