Anomaly Obstructions to Symmetry Preserving Gapped Phases

Abstract

Anomalies are renormalization group invariants that constrain the dynamics of quantum field theories. We show that certain anomalies for discrete global symmetries imply that the underlying theory either spontaneously breaks its generalized global symmetry or is gapless. We identify an obstruction, formulated in terms of the anomaly inflow action, that must vanish if a symmetry preserving gapped phase, i.e. a unitary topological quantum field theory, exits with the given anomaly. Our result is similar to the $2d$ Lieb-Schultz-Mattis theorem but applies more broadly to continuum theories in general spacetime dimension with various types of discrete symmetries including higher-form global symmetries. As a particular application, we use our result to prove that certain $4d$ non-abelian gauge theories at $\theta =\pi$ cannot flow at long distances to a phase which simultaneously, preserves time-reversal symmetry, is confining, and is gapped. We also apply our obstruction to $4d$ adjoint QCD and constrain its dynamics.

arXiv comment35 pages, 9 figures; references added

References in corpus (40)

• Generalized Global Symmetries
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Theta, Time Reversal, and Temperature
• Fermion Path Integrals And Topological Phases
• Deconfined quantum critical points: symmetries and dualities
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Exploring 2-Group Global Symmetries
• On gauging finite subgroups
• Interacting fermionic topological insulators/superconductors in three dimensions
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• Viscoelastic hydrodynamics and holography
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Setting the quantum integrand of M-theory
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• Anomaly constraints on deconfinement and chiral phase transition
• D-branes and K-theory in 2D topological field theory
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Two-flavor adjoint QCD
• Composite fermi liquids in the lowest Landau level
• Magnetohydrodynamics as superfluidity
• Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry
• Anomaly indicators for time-reversal symmetric topological orders
• Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Bosonic Topological Insulators and Paramagnets: a view from cobordisms
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets
• Composite fermion duality for half-filled multicomponent Landau Levels
• Direct Sum Decompositions and Indecomposable TQFT's
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• A possible phase for adjoint QCD

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