Is the chiral U(1) theory trivial?

TL;DR

This paper argues that the chiral U(1) theory remains non-interacting and trivial in the continuum limit, similar to the vector theory, despite differences in the effective action.

Contribution

It provides a theoretical argument that the chiral U(1) theory is trivial, extending the known triviality of QED to the chiral case.

Findings

Chiral U(1) theory has an imaginary phase factor in the effective action.

The phase factor does not change the triviality of the theory.

Chiral U(1) theory is non-interacting in the continuum limit.

Abstract

The chiral U(1) theory differs from the corresponding vector theory by an imaginary contribution to the effective action which amounts to a phase factor in the partition function. The vector theory, i.e. QED, is known to be trivial in the continuum limit. It is argued that the presence of the phase factor will not alter this result and the chiral theory is non-interacting as well.