Screening of Z(N)-monopole pairs in gauge theories

The screening of magnetic Z(N)-monopoles and the associated screening length in SU(N) gauge theories is analysed theoretically and computed numerically in the 3d SU(2) theory. The nature of the screening excitations as well as their mass have so far remained inconclusive in the literature. Here we show that the screening mass is identical to the lowest JRPC=0+++ excitation of the 4d Yang-Mills Hamiltonian with one compact direction with period 1/T, the subscript R referring to parity in this direction. We extend the continuum formulation to the lattice, and determine the transfer matrix governing the decay of the spatial monopole correlator at any finite lattice spacing. Our numerical results for SU(2) for the screening mass in the dimensionally reduced (high temperature) theory are compatible with the 0++ glueball mass in 3d SU(2).