Discrete symmetry and 't Hooft anomalies for 3450 model

TL;DR

This paper investigates the discrete symmetry and 't Hooft anomalies of a lattice 3450 model, demonstrating its consistency with anomaly-free chiral U(1) gauge theory in 1+1 dimensions.

Contribution

It identifies exact discrete symmetry in the lattice model and computes the 't Hooft anomalies, confirming the model's suitability for simulating anomaly-free chiral gauge theories.

Findings

Discrete symmetry is exact in the lattice model.

No mixed or self 't Hooft anomalies involving the discrete symmetry.

Lattice model reproduces anomaly-free chiral U(1) gauge theory in the continuum limit.

Abstract

We report our study of the discrete symmetry for lattice 3450 model proposed by Wang and Wen. Lattice 3450 model is expected to describe the anomaly free chiral U(1) gauge theory in 1+1 dimension using 2+1 dimensional domain-wall fermion with gapping interactions for the mirror sector. We find that the lattice model has exact discrete symmetry in addition to U(1) x U(1) symmetry. Assuming the Zumino-Stora procedure works also for discrete symmetry, we compute the full 't Hooft anomaly for the target continuum U(1) chiral gauge theory with the same discrete symmetry. We show that the mixed and self anomalies involving the discrete symmetry are absent, which is consistent with the expectation that the lattice 3450 produces chiral U(1) gauge theory in the continuum limit.