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In physics, a non-invertible symmetry is a symmetry of a quantum field theory that is not described by a group, and which in particular does not have an inverse.
Non-invertible symmetries were first studied in 2-dimensional conformal field theory, where fusion categories govern the fusion rules, rather than a group.
Four-dimensional examples of non-invertible symmetries can be obtained from Maxwell theory with topological theta term, via a combination of its SL(2,Z) duality and a discrete subgroup of its electric or magnetic 1-form symmetry.
References
- Schafer-Nameki, Sakura (2023). "ICTP Lectures on (Non-)Invertible Generalized Symmetries". arXiv:2305.18296 .
- Sela, Orr (2024). "Emergent non-invertible symmetries in N=4 Super-Yang-Mills theory". arXiv:2401.05032 .
External links
- "A New Kind of Symmetry Shakes Up Physics" by Kevin Hartnett, Quanta Magazine
- "Non-Invertible Symmetries and their Representations", video lecture by Sahand Seifnashri at Institute for Advanced Study
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