  There are two cases where QCD string is described by an effective theory of
long strings: the static potential and meson scattering amplitudes in the Regge
regime. I show how the former can be solved in the mean-field approximation,
justified by the large number of space-time dimensions, and argue that it turns
out to be exact for the Nambu--Goto string. By adding extrinsic curvature I
demonstrate how the tachyonic instability of the ground-state energy can be
cured by operators less relevant in the infrared.
