The Yang-Mills spectrum from a 2-level algorithm

We investigate in detail a 2-level algorithm for the computation of 2-point functions of fuzzy Wilson loops in lattice gauge theory. Its performance and the optimization of its parameters are described in the context of 2+1D SU(2) gluodynamics. In realistic calculations of glueball masses, it is found that the reduction in CPU time for given error bars on the correlator at time-separation ∼ 0.2fm, where a mass-plateau sets in, varies between 1.5 and 7 for the lightest glueballs in the non-trivial symmetry channels; only for the lightest glueball (0) is the 2-level algorithm not helpful. For the heavier states, or for larger time-separations, the gain increases as expected exponentially in mt, and the improved accuracy allows us to apply the variational method reliably. We present further physics applications in 2+1 and 3+1 dimensions and for different gauge groups that confirm these conclusions.