The Unitarity Flow Conjecture: An On-shell Approach to the Renormalization Group

TL;DR

This paper introduces the Unitarity Flow Conjecture, suggesting that unitarity constrains the renormalization group flow in quantum field theories, and verifies it in a specific scalar field theory using on-shell methods.

Contribution

It proposes a new conjecture linking unitarity to RG flow and demonstrates its validity at all loops in a massless scalar theory without traditional diagrammatic methods.

Findings

Verifies the conjecture at all loops in massless λφ^4 theory

Uses on-shell techniques without counterterms or Feynman diagrams

Establishes a novel connection between unitarity and RG equations

Abstract

We propose that the broad architecture of the renormalization group flow in quantum field theories is, at least in part, fixed by unitarity. The precise statement is summarized in the Unitarity Flow Conjecture, which states that the non-linear $S$-matrix identities obtained by imposing unitarity imply those needed to derive the renormalization group equations. As a proof of principle, we verify this conjecture to all loops at the leading and subleading logarithmic order in the four-dimensional massless $\lambda\phi^4$ theory using on-shell techniques, without reference to any counterterms or Feynman diagrams.