Enhancement of field renormalization in scalar theories via functional renormalization group

TL;DR

This paper applies the Functional Renormalization Group to scalar theories with O(N) symmetry in four dimensions, analyzing the effective potential and field renormalization, revealing significant non-perturbative effects and dependencies.

Contribution

It introduces a detailed numerical analysis of field renormalization in scalar theories using FRG, highlighting non-perturbative large renormalization effects in the N=4 case.

Findings

Large non-perturbative renormalization of the longitudinal field component in N=4 theory

Dependence of field renormalization on UV cut-off and bare coupling

Effective potential and renormalization functions determined in the broken phase

Abstract

The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the field in the broken phase. In our numerical analysis, the infrared limit, corresponding to the vanishing of the running momentum scale in the equations, is approached to obtain the physical values of the parameters by extrapolation. In the N=4 theory a non-perturbatively large value of the physical renormalization of the longitudinal component of the field is observed. The dependence of the field renormalization on the UV cut-off and on the bare coupling is also investigated.