Anomaly enforced gaplessness and symmetry fractionalization for SpinG symmetries

A bstract Symmetries and their anomalies give strong constraints on renormalization group (RG) flows of quantum field theories. Recently, the identification of a theory’s global symmetries with its topological sector has provided additional constraints on RG flows to symmetry preserving gapped phase...

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Bibliographic Details
Published in:The journal of high energy physics 2024-02, Vol.2024 (2), p.65, Article 65
Main Author: Brennan, T. Daniel
Format: Article
Language:English
Subjects:
Anomalies
Classical and Quantum Gravitation
Elementary Particles
Fermions
Gauge theory
Hilbert space
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Symmetry
Topology
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Summary:A bstract Symmetries and their anomalies give strong constraints on renormalization group (RG) flows of quantum field theories. Recently, the identification of a theory’s global symmetries with its topological sector has provided additional constraints on RG flows to symmetry preserving gapped phases due to mathematical results in category and topological quantum field theory. In this paper, we derive constraints on RG flows from ℤ 2 -valued pure- and mixed-gravitational anomalies that can only be activated on non-spin manifolds. We show that such anomalies cannot be matched by a unitary, symmetry preserving gapped phase without symmetry fractionalization. In particular, we discuss examples that commonly arise in 4 d gauge theories with fermions.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP02(2024)065