Revision 2

Accepted · cosmetic change · record

Changes against revision 1:

Title · changed: Revision 1: Does scale invariance imply conformal invariance in four dimensions; Revision 2: Does scale invariance imply conformal invariance in four dimensions?
Plain: A theory that looks the same at all magnifications usually has a larger symmetry, conformal symmetry. Whether this always holds in four dimensions is not proven.
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).
Settled by: A nonperturbative argument without extra assumptions, or a unitary scale-invariant but non-conformal 4D theory.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: partially-resolved
Status note: Proven to all orders in perturbation theory (2012) and nonperturbatively under extra assumptions (2013); no general proof.
Posed since: 1988

Decisions