Hi Sridhar,

There are a number of interesting differences between physics in 2+1 dimensions and physics in 3+1 dimensions (by n+m dimensions I mean "n spatial dimensions" and "m temporal dimensions"). For example, in 3+1 dimensions a point source of scalar radiation that only exists at one instant in time emits an expanding spherical flash of radiation, whereas the corresponding emission in 2+1 dimensions has a "tail" (called "afterglow"). Another example is that the Riemann curvature tensor is in one-to-one correspondence with the stress-energy-momentum tensor according to the Einstein field equations in 2+1 dimensions. This means that there is no curvature in vacuum regions of 2+1 dimensional spacetime (so there are no gravitational waves in 2+1 dimensional spacetime).

Also see http://www.researchgate.net/post/How_many_dimensions_are_there_in_the_universe