Bose-Fermi correspondence and Kac-Moody algebras in four dimensions

Abstract

The Schwinger terms in current-algebra commutation relations generated by a topological mass term in the Yang-Mills Lagrangian are analyzed. It is shown how the Schwinger terms modify the geometry of gauge-group orbits in the space of vector potentials. In 4+1 space-time dimensions the topological mass leads to a current algebra in 3+1 dimensions which in the case of an external Abelian monopole field is identical to a current algebra constructed from a four-component fermion field. The current algebra is a direct generalization of the standard Kac-Moody algebra in 1+1 dimensions.