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arXiv · 2003.06905

Bosonization based on Clifford algebras and its gauge theoretic interpretation

Arkadiusz Bochniak·Błażej Ruba
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Abstract

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.

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Arkadiusz Bochniak, Błażej Ruba. 2020-03-15. Bosonization based on Clifford algebras and its gauge theoretic interpretation. https://doi.org/10.1007/jhep12(2020)118

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