Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
Apr 19, 2022
61 pages
Published in:
- Commun.Math.Phys. 402 (2023) 1, 489-542
- Published: May 19, 2023
e-Print:
- 2204.09025 [hep-th]
Report number:
- YITP-SB-2022-16,
- MIT/CTP-5423,
- YITP-SB-2022-16,
- MIT/CTP-5423
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Abstract: (Springer)
We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discrete torsion class, and duality and triality defects from gauging in half of spacetime. The universal fusion rules between these non-invertible topological defects and the one-form symmetry surface defects are determined. Interestingly, the fusion coefficients are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases, gauge theories, and Chern-Simons theories. The associativity of these algebras over TQFT coefficients relies on nontrivial facts about 2+1d TQFTs. We further prove that some of these non-invertible symmetries are intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flows. Duality and triality defects are realized in many familiar gauge theories, including free Maxwell theory, non-abelian gauge theories with orthogonal gauge groups, and super Yang-Mills theories.Note:
- 61 pages, 9 figures. v2: minor changes
- field theory: topological
- defect: topological
- torsion: discrete
- gauge field theory: Yang-Mills
- symmetry: global
- defect: condensation
- dimension: 1
- triality
- duality
References(104)
Figures(9)
- [2]