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

A. Nichols
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Abstract

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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A. Nichols. 2003-02-11. Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas. https://doi.org/10.1088/1126-6708%2F2003%2F08%2F040

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