Regularization Ambiguity Problem for the Chern-Simons Shift

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.

7 pages, 1 figure, latex 2e, will appear at Mod. Phys. Lett. A