2019/10/11 by Clay Cordova, Clay Córdova, Cordova, Clay +2 · 6 citations
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el #hep-th #math-ph #math.AT #math.MP
paper · pdf · doi:10.48550/arxiv.1910.04962
35 pages, 9 figures; references added
openalex publication_date 2019/10/11 · arxiv created 2020/01/07 · arxiv updated 2020/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 θ=π 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.