Adjoint string breaking in 4d SU(2) Yang-Mills theory

We compute the static potential of adjoint sources in SU(2) Yang-Mills theo ry in four dimensions by numerical Monte Carlo simulations. Following a rec ent calculation in 2 + 1 dimensions, we employ a Variational approach invol ving string and gluelump operators and obtain clear evidence for string bre aking and the saturation of the potential at large distances. For the strin g breaking scale we find r(b) approximate to 1.25 fm, 2.3r(0), or in units of the lightest glueball, r(b)m(0++) approximate to 9.7. We furthermore res olve the first excitation of the flux-tube and observe its breaking as well . The result for rb is in remarkable quantitative agreement with the three- dimensional one. (C) 2000 Elsevier Science B.V. All rights reserved.