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Publication# Anomalies from the covariant derivative expansion

Abstract

We revisit the calculation of chiral anomalies for global and gauge symmetries in the framework of the covariant derivative expansion (CDE). Due to the presence of UV divergences, the result is an ambiguous quantity that depends on the regularization procedure and the renormalization scheme. We introduce a class of regulators that facilitate a straightforward evaluation of the anomaly exclusively in d = 4 spacetime dimensions using the CDE methodology. We derive a master formula for the anomaly that integrates various known results into a unified framework.

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Related concepts (32)

Related publications (33)

Anomaly (physics)

In quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics, a classical anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking parameter goes to zero. Perhaps the first known anomaly was the dissipative anomaly in turbulence: time-reversibility remains broken (and energy dissipation rate finite) at the limit of vanishing viscosity.

Gauge anomaly

In theoretical physics, a gauge anomaly is an example of an anomaly: it is a feature of quantum mechanics—usually a one-loop diagram—that invalidates the gauge symmetry of a quantum field theory; i.e. of a gauge theory. All gauge anomalies must cancel out. Anomalies in gauge symmetries lead to an inconsistency, since a gauge symmetry is required in order to cancel degrees of freedom with a negative norm which are unphysical (such as a photon polarized in the time direction). Indeed, cancellation occurs in the Standard Model.

Gravitational anomaly

In theoretical physics, a gravitational anomaly is an example of a gauge anomaly: it is an effect of quantum mechanics — usually a one-loop diagram—that invalidates the general covariance of a theory of general relativity combined with some other fields. The adjective "gravitational" is derived from the symmetry of a gravitational theory, namely from general covariance. A gravitational anomaly is generally synonymous with diffeomorphism anomaly, since general covariance is symmetry under coordinate reparametrization; i.

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing nature. The o ...

In the standard model of particle physics, the chiral anomaly can occur in relativistic plasmas and plays a role in the early Universe, protoneutron stars, heavy-ion collisions, and quantum materials. It gives rise to a magnetic instability if the number d ...

In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of the scale symmet ...