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Line Operators of Gauge Theories on Non-Spin Manifolds

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arxiv 1911.00589 v2 pith:Y5VAJZPD submitted 2019-11-01 hep-th cond-mat.str-el

J.P. Ang , Konstantinos Roumpedakis , Sahand Seifnashri This is my paper
classification hep-thcond-mat.str-el
keywords linetheoriesgaugeoperatorsmanifoldsallowednon-spinsets
verification ladder T0 review T1 audit T2 compute T3 formal
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We study four-dimensional gauge theories on oriented and non-spin spacetime manifolds. On such manifolds, each line operator arises only either as a boson or a fermion. Based on physical arguments, a method of systematically assigning spin labels to line operators is proposed, and several consistency checks are performed. This is used to classify all possible sets of allowed line operators -- including their spins -- for gauge theories with simple Lie algebras. The Lagrangian descriptions of the theories with these sets of allowed line operators are given. Finally, the one-form symmetries of these theories are studied by coupling to background gauge fields, and their 't Hooft anomalies are computed.

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Cited by 3 Pith papers

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  1. On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies

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    Bordism computation for K(Z,3) identifies a new mixed perturbative anomaly in 5D and a new Z2 discrete anomaly in 7D for U(1) 1-form symmetries.

  2. Symmetry theta angles and topological Witten effects

    hep-th 2025-06 conditional novelty 7.0 of 10

    Symmetry theta angles are intrinsic, Lagrangian-independent parameters of any non-anomalous Abelian invertible symmetry, and their universal effect is a topological Witten effect that shuffles twisted sectors while pr...

  3. Generalized Symmetries Phase Transitions with Local Quantum Fields

    cond-mat.str-el 2025-06 conditional novelty 6.0 of 10

    The paper shows that local gauge theories in 3+1d and 2+1d can realize SPT, SET, and symmetry-breaking phase transitions for one-form symmetries, including phases distinguished by symmetry fractionalization.

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