Regularization Ambiguity Problem for the Chern-Simons Shift

TL;DR

This paper investigates the regularization ambiguities in the Chern-Simons shift, demonstrating how regulator parity influences the shift and emphasizing the importance of proper regularization choices.

Contribution

It reveals the relationship between regulator parity and the Chern-Simons shift, providing a method to obtain correct shift values through suitable regulator selection.

Findings

The Chern-Simons shift depends on the parity of regulators used.

Proper choice of Pauli-Villars regulators can eliminate the shift.

Naive higher covariant derivative regularization leads to incorrect shift values.

Abstract

We consider the Chern-Simons parameter shift with the hybrid regularization consisting of the higher covariant derivative (HCD) and the Pauli-Villars (PV) regulators. We show that the shift is closely related to the parity of the regulators and get the shift and no-shift results by a suitable choice of the PV regulators. A naive treatment of the HCD term leads incorrect value of the shift.