Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-12-03
Int. J. Mod. Phys. A8 (1993) 5575
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, 1 figure available on request
Scientific paper
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.
Kovner Alex
Rosenstein Baruch
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