## 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} × 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 language | English (US) |
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Article number | 173 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 10 |

DOIs | |

State | Published - 2012 |

Externally published | Yes |

## Keywords

- 1/N expansion
- Field theories in lower dimensions