Action principle for OPE
arXiv:1710.05601 · doi:10.1016/j.nuclphysb.2017.11.013
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.
29 pages, 5 figures, based on conference talks at the meetings "In memoriam Rudolf Haag" in September 2016 and the "Wolfhart Zimmermann memorial symposium" in May 2017; v2: details added concerning geometry of field redefinitions, discussion of degeneracies and normalization issues, references edited, other minor editorial changes, v3: edited para on invariant 2-point tensor structures