W-symmetries on the Homogeneous Space G/U(1)^r

Details W-symmetries on the Homogeneous Space G/U(1)^r W-symmetries on the Homogeneous Space G/U(1)^r

2000-03-07

arxiv.org/abs/hep-th/0003047v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, Latex

Scientific paper

A construction of $W$-symmetries is given only in terms of the nonlocal fields (parafermions ${\ps}_{\al}$), which take values on the homogeneous space $G/U(1)^r$, where $G$ is a simply connected compact Lie group manifold (its accompanying Lie algebra ${\cal G}$ is a simple one of rank $r$). Only certain restriction of the root set of Lie algebra on which the parafermionic fields take values are satisfied, then a consistent and non-trivial extension of the stress momentum tensor may exist. For arbitrary simple-laced algebras, i.e. the $A-D-E$ cases, a more detailed discussion is given. The OPE of spin three primary field are calculated, in which a primary field with spin four is emerging.

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