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

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.

Cited by in corpus (1)

• Multilocal bosonization