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

preprint1992arXivOpen access

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)V(x), in terms of whichthe topological charge is Q=−i4π∫d2xεij∂i(V∗∂iV−c.c.)Q=-\frac{i}{4π}\int d^2x ε_{ij}\partial_i(V^*\partial_i V -c.c.). The VEV of the field VV in the confining phase is nonzero and the charge is the winding number corresponding to homotopy group π1(S1)π_1(S^1). Qurks carry the charge QQ and therefore are topological solitons. The effective Lagrangian for VV is derived in models with adjoint and fundamental quarks. In 3+1 dimensions the explicit expression for VV 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±W^\pm should be confined although with small string tension.

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