Large N and the renormalization group

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.Comment: 13 pages, uses harvmac; Added: one page with further clarification of the main results, discussion of earlier work, and new references. To be published in Phys. Lett.

Gauge Invariance, the Quantum Action Principle, and the Renormalization Group

If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We show that an effective Quantum Action Principle can be formulated in perturbation theory which enables the effective Ward identities to be solved order by order, even if the theory requires non-vanishing subtraction points. The difficulties encountered with non-perturbative approximations are briefly discussed.Comment: 11 pages, latex, no figures, one reference added, version to be published on Phys. Lett.

Transversality of the Gluon Self-Energy at Finite Temperature in General Covariant Gauges

The paper ``Transversality of the Gluon Self-Energy at Finite Temperature in General Covariant Gauges'' has been withdrawn.Comment: Paper withdraw