Large N and Bosonization in Three Dimensions

TL;DR

This paper demonstrates that certain 3D SU(N) gauge theories with adjoint fermions can be bosonized in the large N limit by leveraging volume independence and large N equivalence, resulting in a purely bosonic 2D theory.

Contribution

It shows that 3D gauge theories with adjoint fermions can be bosonized in the large N limit, connecting them to 2D theories via volume independence and large N equivalence.

Findings

Large N volume independence enables bosonization of 3D theories.

3D SU(N) gauge theories are equivalent to 2D gauge theories at large N.

Non-Abelian bosonization yields a local bosonic theory in two dimensions.

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 R^{1,1} x S^{1}_{L} 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.