Quarks as topological defects or what is confined inside a hadron?

TL;DR

This paper proposes a topological defect model for quark confinement, representing quarks as topological solitons with explicit constructions in 2+1 dimensions and qualitative implications for 3+1 dimensions.

Contribution

It introduces a novel topological defect framework for understanding confinement, explicitly constructing topological charges in lower dimensions and discussing qualitative effects in realistic models.

Findings

Quarks are modeled as topological solitons carrying topological charge.

In 2+1 dimensions, a local scalar field V is constructed to describe topological charge.

Qualitative implications for 3+1 dimensions include small photon mass and confinement of W± bosons.

Abstract

We present a picture of confinement based on representation of quarks as pointlike topological defects. The topological charge carried by quarks and confined in hadrons is explicitly constructed in terms of Yang - Mills variables. In 2+1 dimensions we are able to construct a local complex scalar field $V(x)$, in terms of whichthe topological charge is $Q=-\frac{i}{4\pi}\int d^2x \epsilon_{ij}\partial_i(V^*\partial_i V -c.c.)$. The VEV of the field $V$ in the confining phase is nonzero and the charge is the winding number corresponding to homotopy group $\pi_1(S^1)$. Qurks carry the charge $Q$ and therefore are topological solitons. The effective Lagrangian for $V$ is derived in models with adjoint and fundamental quarks. In 3+1 dimensions the explicit expression for $V$ and therefore a detailed picture is not available. However, assuming the validity of the same mechanism wepoint out several interesting qualitative consequences. We argue that in the Georgi - Glashow model or any grand unified model the photon (in the Higgs phase) should have a small nonperturbative mass and $W^\pm$ should be confined although with small string tension.