SU(6) model revisited

TL;DR

This paper investigates the vacuum structure of the SU(6) chiral gauge theory by analyzing 't Hooft anomalies and constructing effective theories, revealing a Z3-valued scalar field for the mixed anomaly.

Contribution

It identifies all 't Hooft anomalies in the SU(6) model and constructs effective theories using Wess-Zumino-Witten terms to encode these anomalies.

Findings

Effective theory with Z3-valued scalar field for the mixed anomaly

Identification of all 't Hooft anomalies in the SU(6) model

Complex structure of the discrete chiral self-anomaly remains unresolved

Abstract

We discuss the vacuum structure of the SU(6) model, a chiral gauge theory, from the perspective of anomaly matching. To this end, we first identify all possible 't Hooft anomalies in the UV theory using the Stora-Zumino procedure. Subsequently, we construct an effective theory by applying the idea of the Wess-Zumino-Witten action to derive the topological terms that encode the 't Hooft anomalies. As a result, we demonstrate that a low-energy effective theory reproducing one of the anomalies, namely the mixed anomaly, is described by a Z3-valued scalar field. On the other hand, the effective theory that accounts for the discrete chiral self-anomaly is significantly more intricate, and elucidating its structure remains an ongoing challenge.