Higher group Weyl Symmetry

TL;DR

This paper explores a higher group generalization of Weyl symmetry in 4D quantum field theories, revealing how it modifies background gauge transformations and relates to current mixing under renormalization group flow.

Contribution

It introduces the concept of higher group Weyl symmetry, showing its role in background gauge transformations and current mixing, extending the understanding of symmetries in quantum field theories.

Findings

Higher group Weyl symmetry modifies 2-form background gauge transformations.

It connects to the mixing of conserved currents under RG flow.

Unified expression of effects in local renormalization group equations.

Abstract

We study a higher group analog of the Weyl symmetry in four-dimensional quantum field theories. A typical example is that the modified transformation of the 2-form background gauge field replaces the operator-valued Weyl anomaly associated with gauging the 0-form global symmetry. It is analogous to the 2-group global symmetry where the modified transformation of the 2-form background gauge field replaces the operator-valued chiral anomaly associated with gauging the 0-form symmetry. The physical origin of the higher group Weyl symmetry is that under the renormalization group flow, the conserved current mixes with the electromagnetic current that couples with the dynamical gauge field. We can express these effects in the local renormalization group equations in a unified manner.