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

2003/02/11 by A. Nichols, Alexander Nichols · 8 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Coulomb #Degenerate energy levels #Electron #Field (mathematics) #Homogeneous space #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Series (stratigraphy) #Spin (aerodynamics) #hep-th

paper · pdf · doi:10.1088/1126-6708/2003/08/040

published in Journal of High Energy Physics 2003(08), 040 (Springer Nature) · 23 pages Latex

arxiv created 2003/02/11 · openalex publication_date 2003/08/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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 ∈ 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.

Citations

• Gravitationally Dressed Conformal Field Theory and Emergence of Logarithmic Operators
• Logarithmic Correlations in Quenched Random Magnets and Polymers
• Curiosities at c=-2
• On Reducible but Indecomposable Representations of the Virasoro Algebra
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• Termination of Multifractal behavior for Critical Disordered Dirac Fermions
• Infinite conformal symmetry in two-dimensional quantum field theory
• PP-waves and logarithmic conformal field theories
• Boundary states in boundary logarithmic CFT
• Critical percolation in finite geometries
• Singletons and logarithmic CFT in ADS/CFT correspondence
• Null Vectors in Logarithmic Conformal Field Theory
• BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY

Cited by

• Toward logarithmic extensions of \widehatsℓ (2)_k conformal field models