Discrete Anomaly and Dynamical Mass in 2+1 dimensional $U(1)_V\times U(1)_A$ Model

TL;DR

This paper investigates how a discrete $Z_2$ anomaly in a (2+1)-dimensional $U(1)_V imes U(1)_A$ gauge theory affects the induced spin and dynamical fermion mass, revealing novel anomaly-induced phenomena.

Contribution

It introduces a parity-invariant $U(1)_V imes U(1)_A$ model demonstrating a mutual Chern-Simons term induced by a $Z_2$ anomaly, analyzing its physical consequences.

Findings

Discrete anomaly induces a mutual Chern-Simons term.

Anomaly affects the induced spin in the model.

Dynamical fermion mass is influenced by the anomaly.

Abstract

We note that in (2+1)-dimensional gauge theories with even number of massless fermions, there is anomalous $Z_2$ symmetry if theory is regularized in a parity-invariant way. We then consider a parity invariant $U(1)_V\times U(1)_A$ model, which induces a mutual Chern-Simons term in the effective action due to $Z_2$ anomaly. The effect of the discrete anomaly is studied in the induced spin and in the dynamical fermion mass.