Baryons as Solitons in Three Dimensional Quantum Chromodynamics

TL;DR

This paper demonstrates that baryons in three-dimensional Quantum Chromodynamics can be modeled as solitons, with their quantum properties and mass splittings computed, revealing agreement with quark model predictions and identifying a dibaryon solution.

Contribution

It introduces a soliton-based description of baryons in 3D QCD, including quantization of collective variables and analysis of their quantum numbers and mass splittings.

Findings

Baryons are fermions or bosons depending on N_c parity.

Flavor quantum numbers match naive quark model predictions.

Identifies a dibaryon solution analogous to the deuteron.

Abstract

We show that baryons of three dimensional Quantum Chromodynamics can be understood as solitons of its effective lagrangian. In the parity preserving phase we study, these baryons are fermions for odd $N_c$ and bosons for even $N_c$, never anyons. We quantize the collective variables of the solitons and there by calculate the flavor quantum numbers, magnetic moments and mass splittings of the baryon. The flavor quantum numbers are in agreement with naive quark model for the low lying states. The magnetic moments and mass splittings are smaller in the soliton model by a factor of $\log {F_\pi\over N_c m_\pi}$. We also show that there is a dibaryon solution that is an analogue of the deuteron. These solitons can describe defects in a quantum anti--ferromagnet.