Extended Sugawara construction for the superalgebras SU(/ital M/+1/vert bar//ital N/+1). II. The third-order Casimir algebra

Journal Article · Sat Jul 15 04:00:00 EDT 1989 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.40.415· OSTI ID:5938539

Bouwknegt, P; Ceresole, A; van Nieuwenhuizen, P; McCarthy, J

The machinery developed in paper I is used to compute the operator-productalgebra (OPA) of an operator constructed from the third-order Casimir invariantof the superalgebra SU(/ital m//vert bar//ital n/). The vertex operator construction ofSU(/ital m//vert bar//ital n/)/sup (1)/ is used to find a realization of the OPA forlevel /ital k/=1 in terms of free bosonic fields only. It turns out that inmany respects the conformal structure of the affinized Lie superalgebraSU(/ital m//vert bar//ital n/)/sup (1)/ is similar to that of theKa/hacek c/-Moody algebra SU(/ital m//minus//ital n/)/sup (1)/. Anintermediate result suggests the occurrence of extended conformal symmetries in/ital bc/ systems, to which we will devote a separate discussion.

• Research Organization: Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139(US); Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794; Physics Department, Brandeis University, Waltham, Massachusetts 02254
• OSTI ID: 5938539
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 40:2; ISSN PRVDA
• Country of Publication: United States
• Language: English

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CONFORMAL INVARIANCE
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
PARTITION FUNCTIONS
SU GROUPS
SYMMETRY GROUPS
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