Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas

Details Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas

2003-02-11

arxiv.org/abs/hep-th/0302075v1

JHEP 0308 (2003) 040

Physics

High Energy Physics

High Energy Physics - Theory

23 pages Latex

Scientific paper

10.1088/1126-6708/2003/08/040

We study a set of chiral symmetries contained in degenerate operators beyond the `minimal' sector of the c(p,q) models. For the operators h_{(2j+2)q-1,1}=h_{1,(2j+2)p-1} at conformal weight [ (j+1)p-1 ][ (j+1)q -1 ], for every 2j \in N, we find 2j+1 chiral operators which have quantum numbers of a spin j representation of SU(2). We give a free-field construction of these operators which makes this structure explicit and allows their OPEs to be calculated directly without any use of screening charges. The first non-trivial chiral field in this series, at j=1/2, is a fermionic or para-fermionic doublet. The three chiral bosonic fields, at j=1, generate a closed W-algebra and we calculate the vacuum character of these triplet models.

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