Deformations and renormalisations of \(W_{\infty}\). (English) Zbl 0719.17019
Summary: Deformations of the infinite N limit of the Zamolodchikov \(W_ N\) algebra are discussed. A recent one, due to Pope, Romans and Shen with nonzero central extensions for every conformal spin is shown to be formally renormalisable to one representable in Moyal bracket form. Another deformation is discovered which, like the algebra of Pope et al. possesses automatic closure, but has nonzero central extension only in the Virasoro subalgebra.
MSC:
| 17B68 | Virasoro and related algebras |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
References:
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