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

Abstract

We compute the static potential of adjoint sources in SU(2) Yang-Mills theory in four dimensions by numerical Monte Carlo simulations. Following a recent calculation in 2+1 dimensions, we employ a variational approach involving string and gluelump operators and obtain clear evidence for string breaking and the saturation of the potential at large distances. For the string breaking scale we find $r_b\approx 1.25\mathrm{fm},2.3r_0$, or in units of the lightest glueball, $r_b{m}_{0++}\approx 9.7$. We furthermore resolve the first excitation of the flux-tube and observe its breaking as well. The result for $r_b$ is in remarkable quantitative agreement with the three-dimensional one.

Comments: 15 pages, 3 figures; increased statistics; gauge-fixing clarified; typos corrected