The string tension, confinement and roughening in SU(3) hamiltonian lattice gauge theory

Abstract

Hamiltonian strong coupling expansions for the string tension and β-functions of SU(3) lattice gauge theory are presented to O( g −24) in 3 + 1 and 2 + 1 dimensions. The 3 + 1 dimensional theory is seen to have a weak coupling region 0 ⩽ g ⩽ 1.05, a narrow crossover region, 1.05 ⩽ g ⩽ 1.50, and a strong coupling region, g ⩾ 1.50. These features follow from the series without the use of extrapolation methods. The numerical relation between the string tension T and Λ mom is obtained, T =(2.50±0.50) Λ mom in good agreement with recent computer simulations. The width of the flux tube is computed to O( g −20) and we find evidence for its divergence (“roughening”) at a coupling g≲ 1.02, inside the weak coupling regime.