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

We study a set of chiral symmetries contained in degenerate operators beyondthe `minimal' sector of the c(p,q) models. For the operatorsh_{(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 ofa spin j representation of SU(2). We give a free-field construction of theseoperators which makes this structure explicit and allows their OPEs to becalculated directly without any use of screening charges. The first non-trivialchiral field in this series, at j=1/2, is a fermionic or para-fermionicdoublet. The three chiral bosonic fields, at j=1, generate a closed W-algebraand we calculate the vacuum character of these triplet models.Comment: 23 pages Late