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Whether this always holds in four dimensions is not proven.","posed_since":"1988","precise":"For a unitary, Poincare-invariant 4D QFT with a well-defined stress tensor, determine whether scale invariance implies conformal invariance nonperturbatively. It is proven in 2D (Polchinski 1988), shown to all orders of perturbation theory in 4D (Luty, Polchinski, Rattazzi; Fortin, Grinstein, Stergiou, 2012), and argued nonperturbatively under assumptions (Dymarsky, Komargodski, Schwimmer, Theisen 2013).","problem_ref":null,"references":"","settled_by":"A nonperturbative argument without extra assumptions, or a unitary scale-invariant but non-conformal 4D theory.","status_note":"Proven to all orders in perturbation theory (2012) and nonperturbatively under extra assumptions (2013); no general proof.","title":"Does scale invariance imply conformal invariance in four 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