# Anomalous Current Due to Weyl Anomaly for Conformal Field Theory

## TL;DR

This paper generalizes the understanding of anomalous currents induced by Weyl anomaly in conformal field theories, deriving transformation laws and extending results to arbitrary scale factors and n-form fields.

## Contribution

It provides a unified derivation of Weyl-anomaly-induced currents for arbitrary conformally flat spaces and extends the analysis to n-form fields.

## Key findings

- Derived the transformation law of current under Weyl transformation.
- Provided a new derivation of boundary anomalous currents.
- Extended the analysis to n-form fields.

## Abstract

Recently it is found that Weyl anomaly leads to new anomalous currents in an external electromagnetic field in the curved spacetime. For simplicity, the initial works mainly focus on weak gravitational fields and the anomalous current is obtained for conformally flat spaces with small scale factors. In this paper, we generalize the results to the case with arbitrary scale factors. Firstly, we derive the transformation law of current under Weyl transformation, from which one can read off the anomalous current in general conformally flat spaces. Secondly, by using the Weyl transformation of currents we provide a new derivation of the Weyl-anomaly-induced current near the boundary. Thus we have obtained the two kinds of anomalous currents in the literature from a unified formula. Finally, we extend the discussions to n-form fields and find similar anomalous currents.