# Heat kernel approach to relations between covariant and consistent currents in chiral gauge theories

## TL;DR

This paper uses the heat kernel method to explicitly evaluate the relationship between covariant and consistent currents and energy-momentum tensors in anomalous chiral gauge theories across various dimensions.

## Contribution

It provides explicit calculations of the functional curl relating these currents and tensors using the heat kernel approach, extending previous results to arbitrary even dimensions.

## Key findings

- Explicit expression for the functional curl in arbitrary even dimensions.
- Evaluation of differences between covariant and consistent currents in 2D and 4D.
- Extension of the relation to gravitational anomalies.

## Abstract

We apply the heat kernel method to relations between covariant and consistent currents in anomalous chiral gauge theories. Banerjee et al. have shown that the relation between these currents is expressed by a "functional curl" of the covariant current. Using the heat kernel method, we evaluate the functional curl explicitly in arbitrary even dimensions. We also apply the heat kernel method to evaluate Osabe and Suzuki's results of the difference between covariant and consistent currents in two and four dimensions. Applying the arguments of Banerjee et al. to gravitational anomalies, we investigate the relationship between the covariant and consistent energy-momentum tensors. The relation is found to be expressed by a functional curl of the covariant energy-momentum tensor.