A Remark on the $N \to$ Infinity Limit of $W(N$) Algebras

Bilal, Adel

doi:10.1016/0370-2693(89)90951-9

A Remark on the $N \to$ Infinity Limit of $W(N$ ) Algebras

Adel Bilal
(
- CERN
)

Jun, 1989

5 pages

Published in:

Phys.Lett.B 227 (1989) 406-410

Published: 1989

DOI:

10.1016/0370-2693(89)90951-9

Report number:

CERN-TH-5425/89

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Abstract: (Elsevier)

The (non-linearly) extended conformal algebras associated with su( N ) ( W N -algebras) contain operators W ̃ k (z) of dimensions k =2,3, …, N . We show that in the N →∞ limit, the quantum (commutator) algebra of the W ̃ k (z) reduces to their classical (Poisson bracket) algebra. In particular, this proves the closure — in the usual non-linear sense — of the quantum W ∞ algebra.

ALGEBRA: CONFORMAL
SYMMETRY: SU(N)
ALGEBRA: REPRESENTATION
EXPANSION 1/N
FIELD THEORY: OPERATOR PRODUCT EXPANSION

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A Remark on the N→N \toN→ Infinity Limit of W(NW(NW(N) Algebras

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A Remark on the $N \to$ Infinity Limit of $W(N$ ) Algebras