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Beyond the Large N Limit: Non-linear W(infinity) as symmetry of the SL(2,R)/U(1) coset model

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arxiv hep-th/9109029 v1 pith:M6V3H3BZ submitted 1991-09-18 hep-th

classification hep-th
keywords non-linearalgebracosetinftylargelimitmodelsymmetry
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abstract

We show that the symmetry algebra of the $SL(2,R)_{k}/U(1)$ coset model is a non-linear deformation of $W_{\infty}$, characterized by $k$. This is a universal $W$-algebra which linearizes in the large $k$ limit and truncates to $W_{N}$ for $k=-N$. Using the theory of non-compact parafermions we construct a free field realization of the non-linear $W_{\infty}$ in terms of two bosons with background charge. The $W$-characters of all unitary $SL(2,R)/U(1)$ representations are computed. Applications to the physics of 2-d black hole backgrounds are also discussed and connections with the KP approach to $c=1$ string theory are outlined.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A universal W-algebra for N=4 super Yang-Mills

    hep-th 2025-06 conditional novelty 7.0 of 10

    Using associativity constraints from OPE bootstrapping, the authors give evidence for a one-parameter W-algebra W∞^{s,s} that conjecturally truncates to the VOA of 4d N=4 SU(N) super Yang-Mills at c = -3(N²-1).

  2. Non-supersymmetric strings on AdS$_3$: a world-sheet perspective

    hep-th 2025-12 conditional novelty 6.0 of 10

    On AdS3×S3×S3×S1, a Wilson-line deformation of the Spin(16)×Spin(16)⋊Z2 heterotic string produces a level-matched tachyon, so the classical moduli space contains unstable regions.

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