Beyond the Frenkel-Kac-Segal construction of affine Lie algebras

Abstract

This contribution reviews recent progress in constructing affine Lie algebras at arbitrary level in terms of vertex operators. The string model describes a completely compactified subcritical chiral bosonic string whose momentum lattice is taken to be the (Lorentzian) affine weight lattice. The main feature of the new realization is the replacement of the ordinary string oscillators by physical DDF operators, whereas the unphysical position operators are substituted by certain linear combinations of the Lorentz generators. As a side result we obtain simple expressions for the affine Weyl translations as Lorentz boosts. Various applications of the construction are discussed.