  We derive 4-dimensional N=4 U(N) supersymmetric Yang-Mills theory from a
3-dimensional Chern-Simons-matter theory with product gauge group U(N)^{2n}.
The latter describes M2-branes probing an orbifold where a torus emerges in a
scaling limit. It is expected that the SL(2, Z) duality of the 4-dimensional
Yang-Mills theory will be shown in M-theory point of view since it is trivially
realized as modular transformations of the torus. Indeed, starting from one
single Chern-Simons-matter theory, we find infinitely many equivalent
4-dimensional theories differing up to T-transformation of the SL(2, Z)
redefinition of the gauge coupling tau=theta/2pi + 4pi i/g^2 and a parity
transformation in 4 dimensions. Although S-transformation can not be shown in
our work, it is important that a part of the SL(2, Z) transformation is
realized via the M2-brane action. Thus we think our work can be a step toward a
proof of Montonen-Olive duality via M2-branes.
