Anomaly Obstructions to Symmetry Preserving Gapped Phases

Oct 10, 2019
35 pages
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Abstract: (arXiv)
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 2d2d 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 4d4d non-abelian gauge theories at θ=π\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 4d4d adjoint QCD and constrain its dynamics.
Note:
  • 35 pages, 9 figures; references added
  • symmetry: global
  • time reversal: symmetry
  • symmetry: discrete
  • gauge field theory: nonabelian
  • space-time: dimension
  • anomaly
  • field theory
  • quantum chromodynamics
  • renormalization group
  • topological
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