Bosonization in higher dimensions

Using the recently discovered connection between bosonization and duality transformations, we give an explicit path- integral representation for the bosonization of a massive fermion coupled to a U(1) gauge potential (such as electromagnetism) in d ⩾ 2 space (D = d + 1 ⩾ 3 spacetime) dimensions. We perform this integral explicitly in the limit of large fermion mass. We find that the bosonic theory is described by a rank d -1 antisymmetric Kalb-Ramond-type gauge potential, whose action is local for d = 2 (given by a Chern-Simons action), but nonlocal for d ⩾ 3. By coupling to a statistical Chern-Simons field for d = 2, we obtain a bosonized formulation of anyons. The bosonic theory may be further dualized to a theory involving purely scalars, for any d, and we show this to be a higher-derivative theory for which the scalar decouples from the U(1) gauge potential.