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Large N and bosonization in three dimensions

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Abstract

Bosonization is normally thought of as a purely two-dimensional phenomenon, and generic field theories with fermions in D > 2 are not expected be describable by local bosonic actions, except in some special cases. We point out that 3D SU(N) gauge theories on \( {{\mathbb{R}}^{1,1 }}\times S_L^1 \) with adjoint fermions can be bosonized in the large N limit. The key feature of such theories is that they enjoy large N volume independence for arbitrary circle size L. A consequence of this is a large N equivalence between these 3D gauge theories and certain 2D gauge theories, which matches a set of correlation functions in the 3D theories to corresponding observables in the 2D theories. As an example, we focus on a 3D SU(N) gauge theory with one flavor of adjoint Majorana fermions and derive the large-N equivalent 2D gauge theory. The extra dimension is encoded in the color degrees of freedom of the 2D theory. We then apply the technique of non-Abelian bosonization to the 2D theory to obtain an equivalent local theory written purely in terms of bosonic variables. Hence the bosonized version of the large N three-dimensional theory turns out to live in two dimensions.

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  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K.

    Aleksey Cherman & Daniele Dorigoni

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Cherman, A., Dorigoni, D. Large N and bosonization in three dimensions. J. High Energ. Phys. 2012, 173 (2012). https://doi.org/10.1007/JHEP10(2012)173

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