Extended chiral algebras in the SU(2)_0 WZNW model
arXiv:hep-th/0112094 · doi:10.1088/1126-6708/2002/04/056
Abstract
We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure. Moreover on Hamiltonian reduction these SU(2)_0 W-algebras exactly reduce to those found in c=-2. We explicitly find the free field representations for the chiral j=2 and j=3 operators which have respectively a fermionic doublet and bosonic triplet nature. The correlation functions of these operators accounts for the rational solutions of the Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full algebra of the j=2 operators and find that the associativity of the algebra is only guaranteed if certain null vectors decouple from the theory. We conjecture that these algebras may produce a quasi-rational conformal field theory.
18 pages LATEX. Minor corrections. Full j=2 algebra added
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- Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
- Extended multiplet structure in Logarithmic Conformal Field Theories
- The origin of multiplets of chiral fields in SU(2)_k WZNW at rational level
- Two-Point Functions and Logarithmic Boundary Operators in Boundary Logarithmic Conformal Field Theories
- Two-Point Functions and Boundary States in Boundary Logarithmic Conformal Field Theories