Non-linear Lie conformal algebras with three generators

Details Non-linear Lie conformal algebras with three generators Non-linear Lie conformal algebras with three generators

2007-10-11

arxiv.org/abs/0710.2281v2

Selecta Math.14:163-198,2009

Physics

Mathematical Physics

36 pages, v2 minor changes

Scientific paper

10.1007/s00029-008-0058-8

We classify certain non-linear Lie conformal algebras with three generators, which can be viewed as deformations of the current Lie conformal algebra of sl_2. In doing so we discover an interesting 1-parameter family of non-linear Lie conformal algebras R_{-1}^d and the corresponding freely generated vertex algebras V_{-1}^d, which includes for d=1 the affine vertex algebra of sl_2 at the critical level k=-2. We construct free-field realizations of the algebras V_{-1}^d extending the Wakimoto realization of the affine vertex algebra of sl_2 at the critical level, and we compute their Zhu algebras.

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