Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry

Abstract

We prove that in $(3+1)d$ quantum field theories with ${\mathbb{Z}}_N$ symmetry, certain anomalies forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, this applies to discrete chiral symmetries which are frequently present in gauge theories as we illustrate in examples. Our results also constrain the long-distance behavior of certain condensed matter systems such as Weyl-semimetals and may have applications to crystallographic phases with symmetry protected topological order. These results may be viewed as analogs of the Lieb-Schultz-Mattis theorem for continuum field theories.

arXiv comment4 pages, 1 figure

References in corpus (25)

• Weyl Semimetal in a Topological Insulator Multilayer
• Dirac semimetal in three dimensions
• Quantum Hall effects in a Weyl Semi-Metal: possible application in pyrochlore Iridates
• Deconfined quantum critical points: symmetries and dualities
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Interacting fermionic topological insulators/superconductors in three dimensions
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• The "Parity" Anomaly On An Unorientable Manifold
• Dai-Freed anomalies in particle physics
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Setting the quantum integrand of M-theory
• Symmetry Protected Topological phases and Generalized Cohomology
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• On the cobordism classification of symmetry protected topological phases
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Two-flavor adjoint QCD
• Composite fermi liquids in the lowest Landau level
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models
• Composite fermion duality for half-filled multicomponent Landau Levels
• Discrete gauge anomalies revisited
• Pin TQFT and Grassmann integral

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• Global anomaly matching in higher-dimensional ${\mathbb{CP}}^{N-1}$ model
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy
• Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase
• Anomaly constraint on chiral central charge of (2+1)d topological order
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
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