On \epsilon-conjecture in a-theorem

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.Comment: 5 pages, v2: clarifications added to emphasize that we have no intention of invalidating the derivation by Komargodski and Schwimmer when the renormalization group flow is between two conformal field theorie