Non-invertible symmetry

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.^[1]

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.^[2]

References

^ Schafer-Nameki, Sakura (2023). "ICTP Lectures on (Non-)Invertible Generalized Symmetries". arXiv:2305.18296 [hep-th].
^ Sela, Orr (2024). "Emergent non-invertible symmetries in N=4 Super-Yang-Mills theory". arXiv:2401.05032 [hep-th].

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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[SSN-1] Schafer-Nameki, Sakura (2023). "ICTP Lectures on (Non-)Invertible Generalized Symmetries". arXiv:2305.18296 [hep-th].

[SYM-2] Sela, Orr (2024). "Emergent non-invertible symmetries in N=4 Super-Yang-Mills theory". arXiv:2401.05032 [hep-th].

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