Action principle for OPE

Hollands, Stefan (Institut für Theoretische Physik, Universität Leipzig, Brüderstr. 16, Leipzig, D-04103, Germany)

23 November 2017

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.

Published in: Nuclear Physics B (2017)
Published by: Elsevier
DOI: 10.1016/j.nuclphysb.2017.11.013
License: CC-BY-3.0

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