Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
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Author(s)
Choi, Yichul
Córdova, Clay
Hsin, Po-Shen
Lam, Ho T.
Shao, Shu-Heng
Date Issued
May 19, 2023
Publisher
Springer Berlin Heidelberg
Citation
Choi, Yichul, Córdova, Clay, Hsin, Po-Shen, Lam, Ho T. and Shao, Shu-Heng. 2023. "Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions."
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Author's final manuscript
Abstract
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/s00220-023-04727-4
