Fusion category symmetry. Part II. Categoriosities at c= 1 and beyond
A bstract We study generalized symmetries of quantum field theories in 1+ 1D generated by
topological defect lines with no inverse. This paper follows our companion paper on gapped …
topological defect lines with no inverse. This paper follows our companion paper on gapped …
What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetry
SH Shao - arxiv preprint arxiv:2308.00747, 2023 - arxiv.org
We survey recent developments in a novel kind of generalized global symmetry, the non-
invertible symmetry, in diverse spacetime dimensions. We start with several different but …
invertible symmetry, in diverse spacetime dimensions. We start with several different but …
Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
We discuss the exact non-invertible Kramers-Wannier symmetry of 1+ 1d lattice models on a
tensor product Hilbert space of qubits. This symmetry is associated with a topological defect …
tensor product Hilbert space of qubits. This symmetry is associated with a topological defect …
Topological defect lines and renormalization group flows in two dimensions
A bstract We consider topological defect lines (TDLs) in two-dimensional conformal field
theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs …
theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs …
Duality defects in E8
IM Burbano, J Kulp, J Neuser - Journal of High Energy Physics, 2022 - Springer
A bstract We classify all non-invertible Kramers-Wannier duality defects in the E 8 lattice
Vertex Operator Algebra (ie the chiral (E 8) 1 WZW model) coming from ℤ m symmetries. We …
Vertex Operator Algebra (ie the chiral (E 8) 1 WZW model) coming from ℤ m symmetries. We …
Gauging non-invertible symmetries: topological interfaces and generalized orbifold groupoid in 2d QFT
A bstract Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it
connects distinct theories and also reveals hidden structures in a given theory. We initiate a …
connects distinct theories and also reveals hidden structures in a given theory. We initiate a …
Non-invertible duality defect and non-commutative fusion algebra
Y Nagoya, S Shimamori - Journal of High Energy Physics, 2023 - Springer
A bstract We study non-invertible duality symmetries by gauging a diagonal subgroup of a
non-anomalous U (1)× U (1) global symmetry. In particular, we employ the half-space …
non-anomalous U (1)× U (1) global symmetry. In particular, we employ the half-space …
On triality defects in 2d CFT
DC Lu, Z Sun - Journal of High Energy Physics, 2023 - Springer
A bstract We consider the triality fusion category discovered in the c= 1 Kosterlitz-Thouless
theory [1]. We analyze this fusion category using the tools from the group theoretical fusion …
theory [1]. We analyze this fusion category using the tools from the group theoretical fusion …
Topological defects on the lattice: I. The Ising model
In this paper and its sequel, we construct topologically invariant defects in two-dimensional
classical lattice models and quantum spin chains. We show how defect lines commute with …
classical lattice models and quantum spin chains. We show how defect lines commute with …
On lattice models of gapped phases with fusion category symmetries
K Inamura - Journal of High Energy Physics, 2022 - Springer
A bstract We construct topological quantum field theories (TQFTs) and commuting projector
Hamiltonians for any 1+ 1d gapped phases with non-anomalous fusion category …
Hamiltonians for any 1+ 1d gapped phases with non-anomalous fusion category …