Structure of irreducible SU(2) parafermion modules derived via the Feigin-Fuchs construction

Journal Article · Tue Mar 10 04:00:00 EST 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92000533· OSTI ID:5480093

Griffin, P A ^[1]; Hernandez, O F ^[2]

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1. Fermi National Accelerator Lab., Batavia, IL (US)
2. Dept. of Physics, Univ. of Wisconsin-Madison, Madison, WI (US)

This paper shows how the Feigin-Fuchs Coulomb-gas construction, with two free Gaussian bosons, can be used to derive the representation theory of the SU(2) parafermion models. The authors identify the generators of the chiral algebra within the bosonic Fock space and derive the chiral algebra of the finitely reducible models, which correspond to the SU(2) and SU(1,1) parafermion algebras. The authors then focus on the SU(2) highest-weight modules in the remainder of the paper. Unitary of the modules requires that the states of the parafermion theory be independent of the zero modes of two fermionic vertex operators of the bosonic theory. The expressions for the Virasoro highest weights of the models are doubly degenerate in the bosonic Fock space. The authors formulate the correlation functions of these operators in the parafermion Hilbert space, and in particular, the fusion rules for the Virasoro highest weights are derived in an elegant way. Finally, the irreducible parafermion characters are derived. The authors discuss the connection between out analysis and previous work on representation theory based on BRST cohomology.

• OSTI ID: 5480093
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 77:6; ISSN 0217-751X; ISSN IMPAE
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
BOSONS
CHIRAL SYMMETRY
CORRELATION FUNCTIONS
COULOMB FIELD
ELECTRIC FIELDS
ELECTRON GAS
FERMIONS
FLUIDS
FUNCTIONS
GASES
GAUSS FUNCTION
HILBERT SPACE
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL SPACE
SPACE
SU GROUPS
SU-2 GROUPS
SYMMETRY
SYMMETRY GROUPS
UNITARITY