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Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
- Source :
- Communications in Mathematical Physics.
- Publication Year :
- 2023
- Publisher :
- Springer Science and Business Media LLC, 2023.
-
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, $\mathbb{Z}_N$ gauge theories, and $U(1)_N$ 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, ${\cal N}=1,$ and ${\cal N}=4$ super Yang-Mills theories.<br />61 pages, 9 figures. v2: minor changes
- Subjects :
- High Energy Physics - Theory
High Energy Physics::Theory
Condensed Matter - Strongly Correlated Electrons
High Energy Physics - Theory (hep-th)
Strongly Correlated Electrons (cond-mat.str-el)
Mathematics - Quantum Algebra
FOS: Mathematics
Quantum Algebra (math.QA)
FOS: Physical sciences
Statistical and Nonlinear Physics
Mathematical Physics
Subjects
Details
- ISSN :
- 14320916 and 00103616
- Database :
- OpenAIRE
- Journal :
- Communications in Mathematical Physics
- Accession number :
- edsair.doi.dedup.....c2f36864749538f005c8d7ee7c63f22d