Bosonization based on Clifford algebras and its gauge theoretic interpretation

We study the properties of a bosonization procedure based on Clifford algebra valued degrees of freedom, valid for spaces of any dimension. We present its interpretation in terms of fermions in presence of $\mathbb{Z}_2$ gauge fields satisfying a modified Gauss' law, resembling Chern-Simons-like theories. Our bosonization prescription involves constraints, which are interpreted as a flatness condition for the gauge field. Solution of the constraints is presented for toroidal geometries of dimension two. Duality between our model and $(d-1)$-form $\mathbb{Z}_2$ gauge theory is derived, which elucidates the relation between the approach taken here with another bosonization map proposed recently.