Large N and the renormalization group

Details Large N and the renormalization group Large N and the renormalization group

1997-04-11

arxiv.org/abs/hep-th/9704094v3

Phys.Lett. B409 (1997) 363-370

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, uses harvmac; Added: one page with further clarification of the main results, discussion of earlier work, and new re

Scientific paper

10.1016/S0370-2693(97)00866-6

In the large N limit, we show that the Local Potential Approximation to the flow 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 relation between the Polchinski and Legendre effective potentials (that holds for all N), we find the correct large N limit of these flow equations. We also show that all forms (and all parts) of the renormalization group are exactly soluble in the large N limit, choosing as an example, D dimensional O(N) invariant N-component scalar field theory.

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