The Renormalization Group and the Effective Action

The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function beta, the next-to-leading-log (NLL) contributions in terms of the two-loop RG function etc. The log independent pieces are not determined by the RG equation, but can be fixed by the anomaly in the trace of the energy-momentum tensor. Similar considerations can be applied to the effective potential V for a scalar field phi; here the log independent pieces are fixed by the condition V'(phi=v)=0

Renormalization Group Determination of the Five-Loop Effective Potential for Massless Scalar Field Theory

The five-loop effective potential and the associated summation of subleading logarithms for O(4) globally-symmetric massless $\lambda\phi^4$ field theory in the Coleman-Weinberg renormalization scheme $\frac{d^4V}{d\phi^4}|_{\phi = \mu} = \lambda$ (where $\mu$ is the renormalization scale) is calculated via renormalization-group methods. An important aspect of this analysis is conversion of the known five-loop renormalization-group functions in the minimal-subtraction (MS) scheme to the Coleman-Weinberg scheme.Comment: 5 pages. Write-up of talk given at Theory Canada III, June 2007, University of Albert