Scale v.s. conformal invariance in four dimensions
Abstract: I argue that every unitary scale invariant theory is conformally invariant in four dimensions.
The argument follows that of Luty, Polchinski and Rattazzi, and is based on additional assumptions that:
(1) A kind of crossing symmetry for vanishing matrix elements holds regardless of the existence of the S-matrix. (2) Correlation functions in momentum space are analytic functions other than singularities and branch cuts coming from on-shell processes. (3) The Wightman axioms are sufficient criteria of the locality of an operator.
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