Physics / research
Extended operators and generalized symmetry
Extend symmetry reasoning to line and surface observables, topological actions, anomalies, and dualities with careful attention to dimensions and operator definitions.
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Module 01 research
Extended operators and generalized symmetry
Extend symmetry reasoning to line and surface observables, topological actions, anomalies, and dualities with careful attention to dimensions and operator definitions.
- 01
Higher-form symmetry charges and defects
Track the degrees of conserved currents, topological symmetry operators, charged insertions, and background fields in a declared spacetime dimension.
35 min - 02
Wilson and ’t Hooft line operators
Define electric holonomy probes and magnetic disorder lines in compact four-dimensional gauge theory, keeping their allowed charges and global form explicit.
35 min - 03
Electric and magnetic one-form symmetries
Identify the two closed flux forms of source-free compact Maxwell theory and track how dynamical charges reduce the exact generalized symmetry.
35 min - 04
Spontaneous breaking of generalized symmetries
Use charged-loop scaling and the order of limits to distinguish an exact generalized symmetry from its unbroken or broken realization.
35 min - 05
Background higher-form gauge fields
Couple a one-form global symmetry to a two-form background, distinguish background redundancy from gauging, and construct a gauge-invariant dressed line.
35 min - 06
Chern–Simons action and level quantization
Define compact abelian Chern–Simons theory globally, distinguish spin and bosonic level conditions, and calculate oriented line phases with an explicit action sign.
35 min - 07
Abelian BF theory and linking observables
Compute line–surface phases and topological sectors in four-dimensional compact BF theory, with quantized fields and oriented linking specified.
35 min - 08
Topological defects and fusion rules
Describe how topological defects compose, distinguish direct-sum multiplicities from probabilities, and identify what a fusion ring leaves unspecified.
35 min - 09
Noninvertible symmetry in solvable examples
Use the critical Ising topological-line algebra to distinguish a simple noninvertible symmetry defect from a reducible sum or a unitary time-evolution operator.
35 min - 10
Generalized anomaly constraints on phases
Derive a mixed one-form background variation, cancel it by five-dimensional inflow, and state the resulting limits on symmetric infrared phases.
35 min