Effective potential in leading logarithmic approximation in non-renormalisable $SO(N)$ scalar field theories

TL;DR

This paper investigates the effective potential in non-renormalisable scalar SO(N) theories using leading logarithmic approximation, deriving recurrence relations and RG equations, some of which are solvable exactly.

Contribution

It introduces a method to analyze the effective potential in non-renormalisable theories via recurrence relations and generalized RG equations, with exact solutions in special cases.

Findings

Recurrence relations for leading logarithm coefficients derived

Generalized RG equations formulated and analyzed

Exact solutions obtained in specific scenarios

Abstract

The study of the effective potential for non-renormalisable scalar SO(N) symmetric theories leads to recurrence relations for the coefficients of the leading logarithms. These relations can be transformed into generalised renormalization-group (RG) equation which can be analyzed in detail. In some special cases this equation can be solved exactly.