Bosonic realization of toroidal Lie algebras of classical types

Abstract

Generalizing Feingold-Frenkel's construction we use Weyl bosonic fields to construct toroidal Lie algebras of types $A_n,B_n$, $C_n$ and $D_n$ of level $-1,-2,-1/2$ and -2 respectively. In particular, our construction also gives new bosonic construction for the orthogonal Lie algebras in the cases of affine Lie algebras.