  Based on the recent proposal of N=8 superconformal gauge theories of the
multiple M2 branes, we derive (2+1)-dimensional supersymmetric Janus field
theories with a space-time dependent coupling constant. From the original
Bagger-Lambert model, we get a supersymmetric field theory with a similar
action to the N D2 branes, but the coupling varies with the space-time as a
function of the light-cone coordinate, g(t+x). Half of the supersymmetries can
be preserved. We further investigate the M2 brane action deformed by mass and
Myers-like terms. In this case, the final YM action is deformed by mass and
Myers terms and the coupling behaves as exp(\mu x) where \mu is a constant mass
parameter. Weak coupling gauge theory is continuously changed to strong
coupling in the large x region.
