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On the structure of unitary conformal field theory. I: Existence of conformal blocks. (English) Zbl 0683.46053

Summary: We study the general mathematical structure of unitary rational conformal field theories in two dimensions, starting from the Euclidean Green functions of the scaling fields. We show that, under certain assumptions, the scaling fields of such theories can be written as sums of products of chiral fields. The chiral fields satisfy an algebra whose structure constants are the matrix elements of Yang-Baxter- or braid-matrices whose properties we analyze. The upshot of our analysis is that two-dimensional conformal field theories of the type considered in this paper appear to be constructible from the representation theory of a pair of chiral algebras.

MSC:

46N99 Miscellaneous applications of functional analysis
81T08 Constructive quantum field theory
17B99 Lie algebras and Lie superalgebras
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