On є-Conjecture in α-Theorem

Abstract

The derivation of the α-theorem recently proposed by Komargodski and Schwimmer relies on the ϵ-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 dimensions. Thus, a complete proof of the α-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.

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