Beyond the Frenkel-Kac-Segal construction of affine Lie algebras
R. W. Gebert (IAS, Princeton, U.S.A.)
TL;DR
This paper reviews a novel construction of affine Lie algebras at any level using vertex operators within a compactified string model, replacing oscillators with DDF operators and deriving new Lorentz boost expressions.
Contribution
It introduces a new realization of affine Lie algebras via vertex operators, replacing string oscillators with DDF operators and connecting affine Weyl translations to Lorentz boosts.
Findings
New vertex operator-based construction of affine Lie algebras
Expressions for affine Weyl translations as Lorentz boosts
Application of the construction to various models
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.
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