Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
By Yichul Choi, Clay Córdova, Po-Shen Hsin, Ho Tat Lam, Shu-Heng Shao. Communications in Mathematical Physics, 2022
203 citations recorded by the source corpus.
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, $${\mathbb {Z}}_N$$ Z N gauge theories, and $$U(1)_N$$ U ( 1 ) N 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, $${{{\mathcal {N}}}}=1,$$ N = 1 , and $${{{\mathcal {N}}}}=4$$ N = 4 super Yang-Mills theories.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/4718f28f218880799eca6846bbdbda783d8e388d
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In Atomic and Molecular Physics, and Optics
In Nuclear and High Energy Physics
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- Sakura Schafer-Nameki
- Jingxiang Wu
- T. Weigand
- Eran Palti
- Thomas W. Grimm
- Chris Mayrhofer
Citations in the corpus
- Universal Non‐Invertible Symmetries (2022, methodology): “In section 4 we study the relation of the above dual symmetries C 2 for S = Γ (0) being a finite 0-form symmetry to the condensation defects constructed using higher gauging of other symmetries [6, 7].”