Color distribution of confining electric flux in Abelian projection gauges

A numerical test is carried out on one of the predictions of ’t Hooft’s ‘‘Abelian projection’’ theory of quark confinement via monopole condensation. This theory predicts that in certain gauges the color-electric field $E_k^{\mathrm{ab}}$ of a confining flux tube is diagonal in the color indices ab. Diagonality of the E field is tested by Monte Carlo simulation of SU(2) lattice gauge theory, using a field-strength gauge ($F_{12}$ diagonal) proposed by ’t Hooft, and also the ‘‘maximal Abelian gauge’’ of Kronfeld et al. In the field-strength gauge it is found that the color distribution of the confining electric field is completely random, while in the maximal Abelian gauge there is only a rather modest enhancement of the diagonal component above its random value, at coupling β=2.4. These data do not support the validity of the Abelian projection theory.