Operator algebras and conformal field theory

Gabbiani, Fabrizio; Frohlich, Jurg

doi:10.1007/BF02096729

Operator algebras and conformal field theory

Fabrizio Gabbiani
(
- Zurich, ETH
)
,
Jurg Frohlich
(
- Zurich, ETH
)

Dec 7, 1992

110 pages

Published in:

Commun.Math.Phys. 155 (1993) 569-640

DOI:

10.1007/BF02096729

Report number:

ETH-TH-92-30

reference search139 citations

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Abstract: (Springer)

We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III1 factor. The conformal net determined by the algebras of local observables is proven to satisfy Haag duality. The representation of the Moebius group (and presumably of the entire Virasoro algebra) on the vacuum sector of a conformal field theory is uniquely determined by the Tomita-Takesaki modular operators associated with its vacuum state and its conformal net. We then develop the theory of Moebius covariant representations of a conformal net, using methods of Doplicher, Haag and Roberts. We apply our results to the representation theory of loop groups. Our analysis is motivated by the desire to find a “background-independent” formulation of conformal field theories.

review
field theory: conformal
operator: algebra
dimension: 2
vacuum state
algebra: representation
loop space
superselection rule
braid group
bibliography

References(87)

Figures(0)

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