Duality and bosonisation in arbitrary dimensions

A functional integral approach is developed to discuss the bosonisation of the massive Thirring and the massive Schwinger models in arbitrary D dimensions. It is found that these models, to all orders in the inverse fermi mass, bosonise to a theory involving a usual gauge field and a (D-2) rank antisymmetric (Kalb-Ramond) tensor field. Explicit bosonisation identities for the fermion current are deduced. Specializing to the lowest order reveals (for any D greater than or equal to 4) a mapping between the massive Thirring model and the Proca model. It also establishes an exact duality between the Proca model and the massive (D - 2) rank Kalb-Ramond model. Schwinger terms in the current algebra are computed. Conventional bosonisation results in D = 2, 3 are reproduced.