Nonperturbative infrared finiteness in super-renormalisable scalar quantum field theory

TL;DR

This paper investigates the infrared behavior of a three-dimensional super-renormalisable scalar quantum field theory, providing nonperturbative evidence that the theory remains IR finite due to the coupling constant acting as an IR regulator.

Contribution

The study combines lattice simulations and data analysis to support the conjecture that super-renormalisable theories are nonperturbatively IR finite, resolving ambiguities present in perturbative approaches.

Findings

Critical mass diverges logarithmically at two loops in perturbation theory.

Lattice simulations suggest the theory is IR finite nonperturbatively.

Coupling constant acts as an IR regulator, confirming long-standing conjectures.

Abstract

We present a study of the IR behaviour of a three-dimensional super-renormalisable quantum field theory (QFT) consisting of a scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ interaction. A bare mass is required for the theory to be massless at the quantum level. In perturbation theory the critical mass is ambiguous due to infrared (IR) divergences and we indeed find that at two-loops in lattice perturbation theory the critical mass diverges logarithmically. It was conjectured long ago in [Jackiw 1980, Appelquist 1981] that super-renormalisable theories are nonperturbatively IR finite, with the coupling constant playing the role of an IR regulator. Using a combination of Markov-Chain-Monte-Carlo simulations of the lattice-regularised theory, both frequentist and Bayesian data analysis, and considerations of a corresponding effective theory we gather evidence that this is indeed the case.