Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
Action principle for OPE
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abstract
We formulate an "action principle" for the operator product expansion (OPE) describing how a given OPE coefficient changes under a deformation induced by a marginal or relevant operator. Our action principle involves no ad-hoc regulator or renormalization and applies to general (Euclidean) quantum field theories. It implies a natural definition of the renormalization group flow for the OPE coefficients and of coupling constants. When applied to the case of conformal theories, the action principle gives a system of coupled dynamical equations for the conformal data. The last result has also recently been derived (without considering tensor structures) independently by Behan (arXiv:1709.03967) using a different argument. Our results were previously announced and outlined at the meetings "In memoriam Rudolf Haag" in September 2016 and the "Wolfhart Zimmermann memorial symposium" in May 2017.
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An 't Hooft anomaly at general imaginary baryon chemical potential constrains the QCD chiral transition to three minimal CFT scenarios, with the favored one for N_f >= 3 featuring a conformal manifold of theta_B-dependent universality classes with an exactly marginal operator tied to baryon density.
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Local CFTs extremise $F$
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
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Does hot QCD have a conformal manifold in the chiral limit?
An 't Hooft anomaly at general imaginary baryon chemical potential constrains the QCD chiral transition to three minimal CFT scenarios, with the favored one for N_f >= 3 featuring a conformal manifold of theta_B-dependent universality classes with an exactly marginal operator tied to baryon density.