Although our physical world is 3+1 dimensional, curiosity has always driven scientists to study higher dimensional physics. The classic examples of such studies include the 4+1 dimensional generalization of quantum Hall state, and the "periodic table" of topological insulators in all dimensions. These studies are of pure theoretical interests only until last year, when a 4+1 dimensional topological insulator was realized in cold atom systems using the "synthetic techniques". The same technique allows us to explore even higher dimensional states of matter experimentally. In this talk we will discuss the interaction effects in these "synthetic topological insulators" in high dimensions. We realize that the generic interaction in this system takes a special form which is very different from ordinary condensed matter systems, and it has strong implications on the classification and phenomena of these synthetic topological insulators.