Kac-Moody Algebra is Hidden Symmetry of Chiral Models

Abstract

The infinite parameter Kac-Moody algebra $\mathsf{C}\mathrm{}\left[t\right]\mathrm{}\otimes G$, whose elements are loops in $G$ and which is related to the vertex operator for the string model when $G=\mathrm{sl}\mathrm{}\left(2c\right)\mathrm{}$, is identified as the hidden-symmetry algebra of the two-dimensional chiral models. These observations suggest that a Kac-Moody Lie algebra is the hidden symmetry of Yang-Mills fields, a phenomenon which, if true, might lead to complete integrability and nonperturbative information. This algebra, also relevant to integrable soliton theory, may elucidate the classical and quantum inverse method for the chiral theory.