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

Arun Debray, Matthew Yu, Weicheng Ye

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.

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

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.
Paper Structure (1 section, 2 theorems, 7 equations, 3 tables)

This paper contains 1 section, 2 theorems, 7 equations, 3 tables.

Table of Contents

  1. End Matter

Key Result

Theorem 1

In 3 spatial dimensions, every quantum anomaly of a finite fermionic symmetry that is captured by supercohomology can be realized by a fermionic topological order using the symmetry extension construction.

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2