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Operators, defects, and symmetries

Compare local and extended operators, defects, and symmetries through their support, defining data, conventions, scope, and canonical owner.

This index is a concise projection, not an independent explanation. Each record keeps the scope needed for use and links to its source page.

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  • Entity class, defining data, support, charge, regime, and collisions require explicit curation and are never inferred solely from titles.
  • The initial records are a small, reviewed set linked to their full treatments.

Coverage note: records included through 2026-08-12

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  • Operator Defect Symmetry

    Higher-form symmetry

    A higher-form symmetry acts on extended charged operators and is characterized only after degree, normalization, topology, and linking data are fixed.

    Collision warning
    The phrase generalized symmetry also includes non-invertible and higher-group structures that are not equivalent to an ordinary p-form symmetry.
    Defining data
    Form degree, current or topological operator, charged-operator dimension, group, normalization, topology, and linking action.
    Canonical exposition
    Open the canonical exposition
    Aliases
    p-form symmetry, generalized global symmetry
    Scope
    Invertible p-form global symmetries and their charged p-dimensional operators.
    Assumptions
    Spacetime dimension, operator support, current degree, charge normalization, allowed cycles, and global form are explicit.
  • Operator Defect Symmetry

    Wilson line

    A Wilson line is an extended gauge observable or probe whose definition depends on a path, representation, connection, and ordering convention.

    Collision warning
    A Wilson loop is a closed Wilson line; lattice Wilson action and Wilsonian renormalization are different uses of the name Wilson.
    Defining data
    Path, orientation, representation, gauge connection, and path ordering.
    Canonical exposition
    Open the canonical exposition
    Canonical treatment
    Wilson Lines and Loops
    Aliases
    Wilson operator, holonomy line
    Scope
    Line-supported operators in gauge theory; open and closed lines have distinct endpoint and gauge-invariance requirements.
    Assumptions
    Gauge group, global form, representation, charge normalization, path orientation, and connection convention are specified by the owner.