Hadron ?

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 which the topological charge is Q = − i 4π d 2 xǫ ij ∂ i (V * ∂ 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 π 1 (S 1). Qurks carry the charge Q and therefore are topological solitons. The phase rotation of V is generated by the operator of magnetic flux. Unlike in QED, the U (1) magnetic flux is explicitly broken by the monopoles. This results in formation of a string between a quark and an antiquark. The effective Lagrangian for V is derived in models with adjoint and fundamental quarks. Baryon is described as a Y-shaped configuration of strings. 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 we point 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. Moreover, W ± should be confined although with small string tension. † NSERC international postdoctoral fellow.