On triviality of $\lambda\phi^4$ quantum field theory in four dimensions

TL;DR

This paper investigates the critical behavior of Euclidean  theory in four dimensions, revealing a linear beta function at strong coupling and discussing implications for the triviality of f quantum field theory.

Contribution

It introduces a non-perturbative mapping from quantum scalar fields in de Sitter space to Euclidean fields, analyzing the beta function's asymptotic behavior at strong coupling.

Findings

Beta function   theory behaves as    at strong coupling

Scaling violations in the beta function are estimated in the strong coupling regime

The analysis supports the triviality of f quantum field theory in four dimensions.

Abstract

Interacting quantum scalar field theories in $dS_D\times M_d$ spacetime can be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_+$ infinity of $dS_D$ spacetime. Using this non-perturbative mapping, we analyze the critical behavior of Euclidean $\lambda\phi_4^4$ theory in the symmetric phase and find the asymptotic behavior $\beta(\lambda)\sim \lambda$ of the beta function at strong coupling. Scaling violating contributions to the beta function are also estimated in this regime.