On triviality of $\lambda {\varphi }^4$ quantum field theory in four dimensions

Abstract

Interacting quantum scalar field theories in $d{S}_D\times M_d$ spacetime can be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_{+}$ infinity of $d{S}_D$ spacetime. Using this non-perturbative mapping, we analyze the critical behavior of Euclidean $\lambda {\varphi }_4^4$ 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.

Comments: 17 pages, 1 fig.