Bosonization based on Clifford algebras and its gauge theoretic interpretation

Understand

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.