From the planar limit to M theory

The large-N limit of gauge theories has been playing a crucial role in theoretical physics over the decades. Despite its importance, little is known outside the planar limit where the 't Hooft couplingλ = g(YM)(2)N is fixed. In this Letter we consider more general large-N limit--λ grows with N, e.g., g(YM)(2) is fixed. Such a limit is important particularly in recent attempts to find the nonpertubative formulation of M theory. Based on various supporting evidence, we propose this limit is essentially identical to the planar limit, in the sense the order of the large-N limit and the strong coupling limit commute. For a wide class of large-N gauge theories, these two limits are smoothly connected, and the analytic continuation from the planar limit is justified. As simple examples, we reproduce a few properties of the six-dimensional N = (2,0) theory on S(1) from the five-dimensional maximal super Yang-Mills theory, supporting the recent conjecture by Douglas and Lambert et al. that these two theories are identical.