For non-invertible on-site symmetries on 2+1D lattices, Haag duality is preserved exactly only for cuspless regions (weak form with collar for cusped regions); disjoint additivity holds for group-based double models and is weakened for general Hopf algebra constraints, including extended string-net
Nets of Subfactors
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
A subtheory of a quantum field theory specifies von~Neumann subalgebras $\aa(\oo)$ (the `observables' in the space-time region $\oo$) of the von~Neumann algebras $\bb(\oo)$ (the `fields' localized in $\oo$). Every local algebra being a (type $\III_1$) factor, the inclusion $\aa(\oo) \subset \bb(\oo)$ is a subfactor. The assignment of these local subfactors to the space-time regions is called a `net of subfactors'. The theory of subfactors is applied to such nets. In order to characterize the `relative position' of the subtheory, and in particular to control the restriction and induction of superselection sectors, the canonical endomorphism is studied. The crucial observation is this: the canonical endomorphism of a local subfactor extends to an endomorphism of the field net, which in turn restricts to a localized endomorphism of the observable net. The method allows to characterize, and reconstruct, local extensions $\bb$ of a given theory $\aa$ in terms of the observables. Various non-trivial examples are given.
citation-role summary
background 1
citation-polarity summary
fields
hep-th 2verdicts
UNVERDICTED 2roles
background 1polarities
background 1representative citing papers
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
citing papers explorer
-
Algebraic locality and non-invertible Gauss laws
For non-invertible on-site symmetries on 2+1D lattices, Haag duality is preserved exactly only for cuspless regions (weak form with collar for cusped regions); disjoint additivity holds for group-based double models and is weakened for general Hopf algebra constraints, including extended string-net
-
Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.