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K. -H. Rehren

Publications and source records attributed to K. -H. Rehren.

26 records · Page 2Linked to original sources
arXiv1997

A nonabelian square root of abelian vertex operators

Kadanoff's "correlations along a line" in the critical two-dimensional Ising model (1969) are reconsidered. They are the analytical aspect of a representation of abelian chiral vertex operators as quadratic polynomials, in the sense of operator valued distributions, in non-abelian exchange fields. This basic result has interesting applications to conformal coset models. It also gives a new explanation for the remarkable relation between the "doubled" critical Ising model and the free massless Dirac theory. As a consequence, analogous properties as for the Ising model order/disorder fields with respect both to doubling and to restriction along a line are established for the two-dimensional local fields with chiral level 2 SU(2) symmetry.

hep-th↗
arXiv1996

Generalized Cuntz algebras associated with subfactors

Various generalizations of Cuntz algebras and their relations to symmetry and duality are reviewed. New generalized Cuntz algebras are associated with a subfactor. A characteristic Hilbert space of basic invariants (with respect to the generalized symmetry) within these algebras is discussed.

funct-an↗
arXiv1996

Weak C* Hopf Symmetry

Weak C* Hopf algebras can act as global symmetries in low-dimensional quantum field theories, when braid group statistics prevents group symmetries. Possibilities to construct field algebras with weak C* Hopf symmetry from a given theory of local observables are discussed.

q-alg↗
arXiv1994

Nets of Subfactors

A subtheory of a quantum field theory specifies von~Neumann subalgebras $å(\oo)$ (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 $å(\oo) \subset \bb(\oo)$ 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 $å$ in terms of the observables. Various non-trivial examples are given.

hep-th↗
arXiv1994

Characterizing Invariants for Local Extensions of Current Algebras

Pairs $å\subset \bb$ of local quantum field theories are studied, where $å$ is a chiral conformal \qft and $\bb$ is a local extension, either chiral or two-dimensional. The local correlation functions of fields from $\bb$ have an expansion with respect to $å$ into \cfb s, which are non-local in general. Two methods of computing characteristic invariant ratios of structure constants in these expansions are compared: $(a)$ by constructing the monodromy \rep of the braid group in the space of solutions of the Knizhnik-Zamolodchikov differential equation, and $(b)$ by an analysis of the local subfactors associated with the extension with methods from operator algebra (Jones theory) and algebraic quantum field theory. Both approaches apply also to the reverse problem: the characterization and (in principle) classification of local extensions of a given theory.

hep-th↗
arXiv1993

Subfactors and coset models

Some facts about von Neumann algebras and finite index inclusions of factors are viewed in the context of local quantum field theory. The possibility of local fields intertwining superselection sectors with braid group statistics is explored. Conformal embeddings and coset models serve as examples. The associated symmetry concept is pointed out.

hep-th↗
arXiv1993

News from the Virasoro algebra

It is shown that the local quantum field theory of the chiral energy- momentum tensor with central charge $c=1$ coincides with the gauge invariant subtheory of the chiral $SU(2)$ current algebra at level 1, where the gauge group is the global $SU(2)$ symmetry. At higher level, the same scheme gives rise to $W$-algebra extensions of the Virasoro algebra.

hep-th↗