Instantons as a bridge between weak and strong coupling in quantum chromodynamics

The transition from weak to strong coupling in quantum chromodynamics is discussed using semiclassical methods to calculate the effective coupling $g\left(a\right)\mathrm{}$ of an effective lattice theory as a function of $a$. We demonstrate that the renormalization effects due to instantons cause a sharp transition from weak to strong coupling in the range $g\left(a\right)\mathrm{}\approx 1.5-3$. This is verified by showing that the "string tension" as well as the $\beta$ function calculated by semiclassical methods match their strong-coupling behavior for $g\approx 1.5-3$. An independent test of this notion is provided by a bag-model calculation of the string tension.