Vertex operators in the conformal field theory on \(\mathbb P^1\) and monodromy representations of the braid group
type: Item
instance of: scholarly article
title: Vertex operators in the conformal field theory on \(\mathbb P^1\) and monodromy representations of the braid group
zbMATH Open document ID: 0631.17010
DOI: 10.1007/BF00401159
author: Akihiro Tsuchiya
author: Yukihiro Kanie
published in: Letters in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: In this note the authors give a rigorous mathematical foundation to the work of \textit{V. G. Knizhnik} and \textit{A. B. Zamolodchikov} [Nucl. Phys., B 247, No. 1, 83--103 (1984; Zbl 0661.17020)] on the primary fields for the two-dimensional conformal field theory. One of the results is the existence and uniqueness theorem of primary fields (vertex operators). A multipoint (correlation) function is defined as a vacuum expectation value of the composition of the primary fields. A system of differential equations and a system of algebraic equations are given, which are satisfied by a multipoint function. Using these equations, analytic continuation of a multipoint function is discussed. Finally the authors state the result that the monodromies on multipoint functions coincide with the representations of the Hecke algebra constructed by Wenzl. Details and proofs will appear in [Conformal field theory and solvable lattice models, Symp., Kyoto/Jap. 1986, Adv. Stud. Pure Math. 16, 297--372 (1988; Zbl 0661.17021)].
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 20F36
zbMATH DE Number: 4025651
zbMATH Keywords: primary fields
zbMATH Keywords: conformal field theory
zbMATH Keywords: vertex operators
zbMATH Keywords: vacuum expectation value
zbMATH Keywords: monodromies on multipoint functions
reviewed by: Hiromichi Yamada
MaRDI profile type: Publication
cites work: Infinite conformal symmetry in two-dimensional quantum field theory
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description: scientific article; zbMATH DE number 4025651