Canonical tensor product subfactors

Canonical tensor product subfactors (CTPS's) describe, among other things, the embedding of chiral observables in two-dimensional conformal quantum field theories. A new class of CTPS's is constructed some of which are associated with certain modular invariants, thereby establishing the expected existence of the corresponding two-dimensional theories.Comment: 14 pages; references added and minor improvement

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.Comment: Latex, 18 pages, DESY 93-11

Algebraic Holography

A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal boundary. The correspondence is given by the explicit identification of observables localized in wedge regions in anti-deSitter space and observables localized in double-cone regions in its boundary. It takes vacuum states into vacuum states, and positive-energy representations into positive-energy representations.Comment: 16 pages, 1 figure, v3: new material added in response to referees' reports, v4: a hasty conclusion in v3 rectified + more cosmetic change

Chiral Observables and Modular Invariants

Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general characteristics of modular invariant partition functions, although SL(2,Z) transformation properties are not assumed. First steps towards classification are made.Comment: 28 pages, 1 figur