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

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.

23 pages Latex

References in corpus (5)

• The su(2)_{-1/2} WZW model and the beta-gamma system
• PP-waves and logarithmic conformal field theories
• The Neveu-Schwarz and Ramond Algebras of Logarithmic Superconformal Field Theory
• Ghost Systems Revisited: Modified Virasoro Generators and Logarithmic Conformal Field Theories
• SU(2)_k Logarithmic Conformal Field Theories

Cited by in corpus (6)

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• Toward logarithmic extensions of ^sl(2)_k conformal field models
• The origin of multiplets of chiral fields in SU(2)_k WZNW at rational level
• Canonical approach to the WZNW model
• 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