TY - JOUR

T1 - Large N and bosonization in three dimensions

AU - Cherman, Aleksey

AU - Dorigoni, Daniele

PY - 2012

Y1 - 2012

N2 - 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 ℝ 1,1 × 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.

AB - 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 ℝ 1,1 × 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.

KW - 1/N expansion

KW - Field theories in lower dimensions

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U2 - 10.1007/JHEP10(2012)173

DO - 10.1007/JHEP10(2012)173

M3 - Article

AN - SCOPUS:84868277206

SN - 1126-6708

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 173

ER -