1,528 research outputs found
Bosonizations of and Integrable Hierarchies
We construct embeddings of in lattice vertex
algebras by composing the Wakimoto realization with the
Friedan-Martinec-Shenker bosonization. The Kac-Wakimoto hierarchy then gives
rise to two new hierarchies of integrable, non-autonomous, non-linear partial
differential equations. A new feature of our construction is that it works for
any value of the central element of ; that is, the
level becomes a parameter in the equations
Non-linear Lie conformal algebras with three generators
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.Comment: 36 pages, v2 minor change
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