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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.
Coverage notes
- 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.
Latest lookup-entry revision: 2026-09-12
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Operator Defect 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.
- 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
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.
- 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.
Original QFT.org content:CC BY 4.0, unless an item supplies different terms. Third-party material retains its own terms.
