Resummation of the Two Distinct Large Logarithms in the Broken $O(N)$-symmetric ${\varphi }^4$-model

Abstract

The loop-expansion of the effective potential in the $O(N)$-symmetric ${\varphi }^4$-model contains generically two types of large logarithms. To resum those systematically a new minimal two-scale subtraction scheme $\tMS$ is introduced in an $O(N)$-invariant generalization of $\MS$. As the $\tMS$ beta functions depend on the renormalization scale-ratio a large logarithms resummation is performed on them. Two partial $\tMS$ renormalization group equations are derived to turn the beta functions into $\tMS$ running parameters. With the use of standard perturbative boundary conditions, which become applicable in $\tMS$, the leading logarithmic $\tMS$ effective potential is computed. The calculation indicates that there is no stable vacuum in the broken phase of the theory for $1<N\le 4$.

11 pages, LaTeX. Talk given at The Third International Conference Renormalization Group - 96, Dubna, Russia, 26 - 31 August 1996