An investigation of Z(2) vortices in SU(2) _{3}
Abstract
For a general lattice gauge theory, we show how the expectation value of any observable may be found by first preaveraging over some chosen set of degrees in freedom and then averaging this result in the conventional functional integral. The restrictions on the selected degrees of freedom are found. With an appropriate choice of degrees of freedom in the preaverage, the preverage gives an upper bound on the expectation value of the Wilson loop in U(1) _{3} which corresponds to the logarithmic Coulomb potential at weak coupling. We then consider the SU(2) case and construct a set of Z(2) vortices as the degrees of freedom to be preaveraged over. For an R by T Wilson loop, the preaveraged value when all links are set to unity falls as exp(ϱTR ^{{1}/{2}}/β ^{{3}/{2}}) , where ϱ is a constant, at large β for large loops. It is unknown whether this behavior for the preaveraged quantity can be used to bound the Wilson loop in SU(2).
 Publication:

Nuclear Physics B
 Pub Date:
 July 1989
 DOI:
 10.1016/05503213(89)902666
 Bibcode:
 1989NuPhB.321..653M