Large N and bosonization in three dimensions

Aleksey Cherman, Daniele Dorigoni

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Article number173
JournalJournal of High Energy Physics
Issue number10
StatePublished - 2012
Externally publishedYes


  • 1/N expansion
  • Field theories in lower dimensions


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