A Unique Determination of the Effective Potential in Terms of Renormalization Group Functions

Understand

The perturbative effective potential V in the massless $\lambda\phi^4$ model with a global O(N) symmetry is uniquely determined to all orders by the renormalization group functions alone when the Coleman-Weinberg renormalization condition $\frac{d^4V}{d\phi^4}|_{\phi = \mu} = \lambda$ is used, where $\mu$ represents the renormalization scale.

• Systematic methods are developed to express the n-loop effective potential in the Coleman-Weinberg scheme in terms of the known n-loop minimal subtraction (MS) renormalization-group functions.
• Moreover, it also proves possible to sum the leading- and subsequent-to-leading-logarithm contributions to V.
• An essential element of this analysis is a conversion of the renormalization group functions in the Coleman-Weinberg scheme to the renormalization group functions in the MS scheme.