LARGE N AND THE RENORMALIZATION-GROUP

In the large N limit, we show that the local potential approximation t o the Row equation for the Legendre effective action, is in effect no longer an approximation, but exact - in a sense, and under conditions, that we determine precisely. We explain why the same is not true for the Polchinski or Wilson flow equations and, by deriving an exact rela tion between the Polchinski and Legendre effective potentials (that ho lds for all N), we find the correct large N limit of these flow equati ons. We also show that all forms (and all parts) of the renormalizatio n group are exactly soluble in the large N limit, choosing as an examp le, D dimensional O(N) invariant N-component scalar field theory. (C) 1997 Published by Elsevier Science B.V.