Large N and bosonization in three dimensions

A bstract 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 with adjoint fermions can...

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Bibliographic Details
Published in:The journal of high energy physics 2012-10, Vol.2012 (10), Article 173
Main Authors: Cherman, Aleksey, Dorigoni, Daniele
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Elementary Particles
Equivalence
Fermions
Gauge theory
High energy physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
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Summary:A bstract 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 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2012)173