63 citations · 270 across the 21 of their papers we have counts for
24 papers
Continuous categories of endomorphisms associated with -kernels
Marcel Bischoff, Pradyut Karmakar
We generalize the construction of tensor categories of endomorphisms of a type III factor associated with a -kernel, from the case of a discrete group to that of a compa…
Anomalies for conformal nets associated with lattices and -kernels
Marcel Bischoff, Pradyut Karmakar
Let an even lattice and the associated torus. Associated with we construct --kernel on a hyperfinite factor type $\m…
Quantum Operations on Conformal Nets
Marcel Bischoff, Simone Del Vecchio, Luca Giorgetti
On a conformal net , one can consider collections of unital completely positive maps on each local algebra , subject to natural compatibility, vacuum p…
Galois Correspondence and Fourier Analysis on Local Discrete Subfactors
Marcel Bischoff, Simone Del Vecchio, Luca Giorgetti
Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a com…
Distortion for multifactor bimodules and representations of multifusion categories
Marcel Bischoff, Ian Charlesworth, Samuel Evington +2
We call a von Neumann algebra with finite dimensional center a multifactor. We introduce an invariant of bimodules over multifactors that we call modular distortion, and…
Compact Hypergroups from Discrete Subfactors
Marcel Bischoff, Simone Del Vecchio, Luca Giorgetti
Conformal inclusions of chiral conformal field theories, or more generally inclusions of quantum field theories, are described in the von Neumann algebraic setting by nets of subfa…
Computing fusion rules for spherical G-extensions of fusion categories
Marcel Bischoff, Corey Jones
A -graded extension of a fusion category yields a categorical action of on the center . If the extension admits a spherical structure, we provid…
A remark about the anomalies of cyclic holomorphic permutation orbifolds
Marcel Bischoff
Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net with central charge $c=8k…
Hopf algebra actions in tensor categories
Marcel Bischoff, Alexei Davydov
We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action all…
Spontaneous symmetry breaking from anyon condensation
Marcel Bischoff, Corey Jones, Yuan-Ming Lu +1
In a physical system undergoing a continuous quantum phase transition, spontaneous symmetry breaking occurs when certain symmetries of the Hamiltonian fail to be preserved in the g…
The rank of -crossed braided extensions of modular tensor categories
Marcel Bischoff
We give a short proof for a well-known formula for the rank of a -crossed braided extension of a modular tensor category.
Conformal Net Realizability of Tambara-Yamagami Categories and Generalized Metaplectic Modular Categories
Marcel Bischoff
We show that all isomorphism classes of even rank Tambara-Yamagami categories arise as -twisted representations of conformal nets. As a consequence, we show that thei…
The hypergroupoid of boundary conditions for local quantum observables
Marcel Bischoff, Karl-Henning Rehren
We review the definition of hypergroups by Sunder, and we associate a hypergroup to a type III subfactor of finite index, whose canonical endomorphism $γ\in\mathrm{End…
Generalized Orbifold Construction for Conformal Nets
Marcel Bischoff
Let be a conformal net. We give the notion of a proper action of a finite hypergroup acting by vacuum preserving unital completely positive (so-called stochastic) map…
The Relation between Subfactors arising from Conformal Nets and the Realization of Quantum Doubles
Marcel Bischoff
We give a precise definition for when a subfactor arises from a conformal net which can be motivated by classification of defects. We show that a subfactor arises fro…
A Remark on CFT Realization of Quantum Doubles of Subfactors. Case Index < 4
Marcel Bischoff
It is well-known that the quantum double of a finite depth subfactor , or equivalently the Drinfeld center of the even part fusion category, is a unitar…
Characterization of 2D rational local conformal nets and its boundary conditions: the maximal case
Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo
Let be a completely rational local Möbius covariant net on , which describes a set of chiral observables. We show that local Möbius covariant nets $\mathcal{B}_2…
Tensor categories and endomorphisms of von Neumann algebras (with applications to Quantum Field Theory)
Marcel Bischoff, Roberto Longo, Yasuyuki Kawahigashi +1
Q-systems describe "extensions" of an infinite von Neumann factor , i.e., finite-index unital inclusions of into another von Neumann algebra . They are (special cases of)…
Phase boundaries in algebraic conformal QFT
Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo +1
We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries…
Integrable QFT and Longo-Witten endomorphisms
Marcel Bischoff, Yoh Tanimoto
Our previous constructions of Borchers triples are extended to massless scattering with nontrivial left and right components. A massless Borchers triple is constructed from a set o…
Construction of wedge-local nets of observables through Longo-Witten endomorphisms. II
Marcel Bischoff, Yoh Tanimoto
In the first part, we have constructed several families of interacting wedge-local nets of von Neumann algebras. In particular, there has been discovered a family of models based o…
Models in Boundary Quantum Field Theory Associated with Lattices and Loop Group Models
Marcel Bischoff
In this article we give new examples of models in boundary quantum field theory, i.e. local time-translation covariant nets of von Neumann algebras, using a recent construction of…
Construction of wedge-local nets of observables through Longo-Witten endomorphisms
Yoh Tanimoto
A convenient framework to treat massless two-dimensional scattering theories has been established by Buchholz. In this framework, we show that the asymptotic algebra and the scatte…
Conformal quantum field theory in various dimensions
Marcel Bischoff, Daniel Meise, Karl-Henning Rehren +1
Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help o…