Bosonization in Higher Dimensions

TL;DR

This paper develops an explicit path-integral bosonization method for massive fermions coupled to U(1) gauge fields in higher dimensions, revealing local and nonlocal actions and connecting to anyon physics.

Contribution

It provides a new explicit bosonization framework in higher dimensions, including a local action in 2D and a nonlocal one in higher dimensions, and links to dual scalar theories.

Findings

Bosonization expressed via a rank d-1 antisymmetric gauge potential.

Local Chern-Simons action for d=2, nonlocal for d>3.

Bosonized theory describes anyons through coupling to Chern-Simons fields.

Abstract

Using the recently discovered connection between bosonization and duality transformations (hep-th/9401105 and hep-th/9403173), 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 space (D=d+1 spacetime) dimensions. The bosonic theory is described by a rank d-1 antisymmetric Kalb-Ramond-type gauge potential. We construct the bosonized lagrangian explicitly in the limit of large fermion mass. We find that the resulting action is local for d=2 (and given by a Chern-Simons action), but nonlocal for d larger than 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 governed by a higher-derivative lagrangian for which the scalar decouples from the U(1) gauge potential.