Symmetric Gapped States and Symmetry-Enforced Gaplessness in 3-dimension

TL;DR

This paper develops a framework to classify 3D fermionic quantum phases based on anomalies, revealing which can be gapped or are symmetry-enforced gapless, and predicts IR phases of certain gauge theories.

Contribution

It introduces a comprehensive anomaly-based classification scheme for 3D fermionic phases, distinguishing gappable and gapless states, and constructs candidate gapped states via symmetry extension.

Findings

Anomalies are divided into two classes: one always admits symmetric gapped states, the other enforces gaplessness.

Constructed candidate gapped states for theories with the first class of anomalies.

Predicted IR phases of (3+1)D gauge theories based on anomaly analysis.

Abstract

We establish a comprehensive framework for characterizing the infrared (IR) phases of a fermionic quantum theory in three spatial dimensions, based on its quantum anomalies associated with a finite symmetry. We uncover a fundamental dichotomy among these anomalies: the first class of anomalies can always be realized by symmetric gapped states, while the second class can never be realized by gapped states without breaking the given symmetry, establishing the phenomenon of symmetry-enforced gaplessness in these settings. Moreover, using the construction of symmetry extension, we construct the candidate gapped states that theories with the first class of anomalies can flow to in the IR. As an application, we provide concrete predictions of the candidate IR phases of (3+1)-dimensional gauge theories based on our results. Our results also suggest that systems with discrete chiral anomalies cannot be gapped out by adding arbitrary bosonic degrees of freedom.