Coherent-state path integrals for loop groups and non-abelian bosonisation

After a discussion of coherent states for the loop group LU(N), we use them to write down a bosonic path integral which describes the level-one representations of LU(N). The construction uses the description of the representations in terms of free right-going Weyl fermions and so provides one with an explicit geometrical interpretation for a Fermi-Bose equivalence. The bosonic system is easily seen to have a single Kac-Moody algebra as its Poisson brackets and coincides with the non-abelian chiral boson model that has been introduced by Sonnenschein et al. [Nucl. Phys. B301 (1988) 346; B309 (1988) 752].