On \epsilon-conjecture in a-theorem

TL;DR

This paper discusses the -conjecture's role in the proof of the a-theorem, highlighting its implications for the equivalence of scale and conformal invariance in four-dimensional quantum field theories.

Contribution

It emphasizes that the decoupling assumption in the -conjecture could prove the equivalence between scale and conformal invariance, linking two major conjectures.

Findings

Decoupling of the dilaton supports the -conjecture.

Proving the -conjecture would establish the equivalence of scale and conformal invariance.

The work connects the a-theorem proof to fundamental symmetry conjectures in QFT.

Abstract

The derivation of the a-theorem recently proposed by Komargodski and Schwimmer relies on the \epsilon-conjecture that demands decoupling of dilaton from the rest of the infrared theory. We point out that the decoupling, if true, provides a strong evidence for the equivalence between scale invariance and conformal invariance in four dimension. Thus, a complete proof of the a-theorem along the line of their argument in the most generic scenario would establish the equivalence between scale invariance and conformal invariance, which is another long-standing conjecture in four-dimensional quantum field theories.