Integer- and Non-Integer-Shift of the Chern-Simons Coupling under a Local Higher Covariant Derivative Regulator

TL;DR

This paper investigates how a local higher covariant derivative regulator affects the shift in the Chern-Simons coupling, revealing that the presence of a Yang-Mills term results in an integer shift, while its absence leads to a non-integer shift.

Contribution

It demonstrates that a local higher covariant derivative regulator can produce non-integer Chern-Simons coupling shifts, highlighting the role of the Yang-Mills term in the shift's integer nature.

Findings

Integer-shift occurs with Yang-Mills term present.

Non-integer shift arises without Yang-Mills term.

The regulator influences the shift value.

Abstract

The Chern-Simons coupling shift is calculated within the framework of the hybrid regularization based on a local higher covariant derivative regulator. When the Yang-Mills term is present in the theory the well-know integer-shift is obtained, but is absent, the shift value is non-integer. These results show a possibility that a non-integer-shift can be derived using a local higher covariant derivative and also suggest that the Yang-Mills term plays an important role in the integer-shift of the Chern-Simons coupling.