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Extended U (1) Conformal Field Theories and Z k ‐Parafermions
Author(s) -
Furlan P.,
Paunov R. R.,
Todorov I. T.
Publication year - 1992
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190400303
Subject(s) - operator product expansion , conformal field theory , current algebra , physics , vertex operator algebra , coulomb , conformal map , virasoro algebra , mathematical physics , central charge , constructive , product (mathematics) , operator (biology) , factorization , vertex (graph theory) , operator algebra , field (mathematics) , minimal models , pure mathematics , algebra over a field , quantum mechanics , mathematics , discrete mathematics , algebra representation , cellular algebra , graph , mathematical analysis , jordan algebra , chemistry , electron , geometry , process (computing) , repressor , algorithm , computer science , operating system , biochemistry , gene , transcription factor
A constructive approach is developed for studying local chiral algebras generated by a pair of oppositely charged fields Ψ (z, ±g) such that the operator product expansion (OPE) of Ψ(z 1 , g) Ψ(z 2 , −g) involves a U (1) current. The main tool in the study is the factorization property of the charged fields (exhibited in [PT 2, 3]) for Virasoro central charge c < 1 into U (1)‐vertex operators tensored with ZAMOLODCHIKOV‐FATEEV [ZF1] (generalized) Z k ‐parafermions. The case Δ 2 = 4 (Δ 1 − 1), where Δ v = Δ k−v (Δ 0 = 0) are the conformaldimensions of the parafermionic currents, is studied in detail. For Δ v = 2 v (1 − v/k ) the theory is related to GEPNER'S [Ge] Z 2 [so ( k )] parafermions and the corresponding quantum field theoretic (QFT) representations of the chiral algebra are displayed. The Coulomb gas method of [CR] is further developed to include an explicit construction of the basic parafermionic current Ψ of weight Δ = Δ 1 . The characters of the positive energy representations of the local chiral algebra are written as sums of products of Kac's string functions and classical θ‐functions.