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**publisher and metadata sources**).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 that give rise to… Continue Reading

Let A be a completely rational local Mobius covariant net on S 1 , which describes a set of chiral observables. We show that local Mobius covari- ant nets B2 on 2D Minkowski space which contain the… Continue Reading

We review the definition of hypergroups by Sunder, and we associate a hypergroup to a type III subfactor $N\subset M$ of finite index, whose canonical endomorphism $\gamma\in\mathrm{End}(M)$ is… Continue Reading

We introduce the tensor category structure of endomorphisms of infinite (type III) von Neumann factors. We review the basic concepts of conjugate homomorphisms between a pair of infinite factors,… Continue Reading

A bstractIn 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 ground… Continue Reading

We review some applications of the abstract theory presented in the preceding chapters in the context of local quantum field theory. The methods developed in Chap. 4 prove to be most efficient to… Continue Reading

Introduction.- Homomorphisms of von Neumann algebras.- Endomorphisms of infinite factors.- Homomorphisms and subfactors.- Non-factorial extensions.- Frobenius algebras, Q-systems and modules.- C*… Continue Reading

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 $N \subset M$ arises from a conformal net… Continue Reading

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 $\mathcal A$ with central charge $c=8k$ depends on the… Continue Reading

ATTENTION: not proof read lecture notes in progress.....