Three Dimensional Quantum Chromodynamics

TL;DR

This paper reviews the study of three-dimensional Quantum Chromodynamics, highlighting phase structure, effective actions, solitonic excitations, and algebraic structures, providing insights into non-perturbative phenomena in lower-dimensional gauge theories.

Contribution

It presents a comprehensive analysis of 3D QCD, including phase behavior, effective actions with solitons, and a novel generalization of Kac-Moody algebras.

Findings

Existence of a parity-preserving phase with specific flavor symmetry breaking

Identification of solitonic excitations with Fermi statistics as baryons

Development of a cohomologically non-trivial algebraic structure in the theory

Abstract

The subject of this talk was the review of our study of three ($2+1$) dimensional Quantum Chromodynamics. In our previous works, we showed the existence of a phase where parity is unbroken and the flavor group $U(2n)$ is broken to a subgroup $U(n)\times U(n)$. We derived the low energy effective action for the theory and showed that it has solitonic excitations with Fermi statistic, to be identified with the three dimensional ``baryon''. Finally, we studied the current algebra for this effective action and we found a co-homologically non trivial generalization of Kac-Moody algebras to three dimensions.