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arXiv · hep-th/9407078

Bosonization in Higher Dimensions

C. P. Burgess·C. A. Lütken·F. Quevedo
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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.

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BibTeXRIS

C. P. Burgess, C. A. Lütken, F. Quevedo. 1994-07-20. Bosonization in Higher Dimensions. https://doi.org/10.1016/0370-2693(94)00963-5

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