Confinement versus asymptotic freedom

Abstract

I put forward the low-energy confining asymptote of the solution $<W_C>$ (valid for large macroscopic contours C of the size $>>1/{\Lambda }_{QCD}$) to the large N Loop equation in the D=4 U(N) Yang-Mills theory with the asymptotic freedom in the ultraviolet domain. Adapting the multiscale decomposition characteristic of the Wilsonean renormgroup, the proposed Ansatz for the loop-average is composed in order to sew, along the lines of the bootstrap approach, the large N weak-coupling series for high-momentum modes with the $N\to \infty$ limit of the recently suggested stringy representation of the 1/N strong-coupling expansion Dub4 applied to low-momentum excitations. The resulting low-energy stringy theory can be described through such superrenormalizable deformation of the noncritical Liouville string that, being devoid of ultraviolet divergences, does not possess propagating degrees of freedom at short-distance scales $<<1/\sqrt{{\sigma }_{ph}}$, where ${\sigma }_{ph}\sim ({\Lambda }_{QCD}{)}^2$ is the physical string tension.

13 pages