The long-range interaction in massless (lambda Phi^4)_4 theory

TL;DR

This paper investigates whether massless (lambda Phi^4)_4 theory exhibits spontaneous symmetry breaking, proposing a nonlocal effective theory with long-range interactions that reconciles different RG-improved results and suggests SSB persists.

Contribution

It introduces a nonlocal effective field theory framework with long-range interactions to analyze SSB in massless (lambda Phi^4)_4 theory, resolving discrepancies in RG-improved results.

Findings

Raw 1-loop result suggests SSB occurs.

RG-improved analysis initially implies no SSB.

Crude calculations within the nonlocal framework support SSB even after RG improvement.

Abstract

Does massless (lambda Phi^4)_4 theory exhibit spontaneous symmetry breaking (SSB)? The raw 1-loop result implies that it does, but the "RG-improved" result implies the opposite. I argue that the appropriate "low-energy effective theory" is a nonlocal field theory involving an attractive, long-range interaction Phi^2(x) Phi^2(y)/z^4, where z=|x-y|. RG improvement then requires running couplings for both this interaction and the original pointlike interaction. A crude calculation in this framework yields SSB even after "RG improvement" and closely agrees with the raw 1-loop result.