Anomalies from an effective field theory perspective

Baptiste Filoche (Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble INP, 38000 Grenoble, France; ENS de Lyon, Université Claude Bernard, 69342 Lyon, France; Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany) ; Rémy Larue (Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble INP, 38000 Grenoble, France; ENS Paris-Saclay, 4, avenue des Sciences, 91190 Gif-sur-Yvette, France) ; Jérémie Quevillon (Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble INP, 38000 Grenoble, France) ; Pham Ngoc Hoa Vuong (Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble INP, 38000 Grenoble, France)

The path-integral measure of a gauge-invariant fermion theory is transformed under the chiral transformation and leads to an elegant derivation of the anomalous chiral Ward-Takahashi identities, as we know from the seminal work of Fujikawa. We present in this work an alternative and illuminating way to calculate the Jacobian in the path-integral measure from the covariant derivative expansion technique used in effective field theory. We present several ways to customize the crucial regularization such that the anomaly is located in the desired current, which is unprecedented within the path integral approach. We are then able to derive, in a transparent and unified way, the covariant, consistent, gravitational, and scale anomalies.

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Published on:
27 January 2023
Publisher:
APS
Published in:
Physical Review D , Volume 107 (2023)
Issue 2
DOI:
https://doi.org/10.1103/PhysRevD.107.025017
arXiv:
2205.02248
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: