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arXiv · 1407.5335

Bosonizations of $\widehat{\mathfrak{sl}}_2$ and Integrable Hierarchies

Bojko Bakalov·Daniel Fleisher
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Abstract

We construct embeddings of $\widehat{\mathfrak{sl}}_2$ 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 $\widehat{\mathfrak{sl}}_2$; that is, the level becomes a parameter in the equations.

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BibTeXRIS

Bojko Bakalov, Daniel Fleisher. 2015-01-14. Bosonizations of $\widehat{\mathfrak{sl}}_2$ and Integrable Hierarchies. https://doi.org/10.3842/sigma.2015.005

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