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 …