Confinement versus asymptotic freedom

TL;DR

This paper proposes a low-energy confining solution for the large N loop equation in 4D Yang-Mills theory, combining weak-coupling series with a stringy representation to describe confinement without short-distance propagating degrees of freedom.

Contribution

It introduces a novel Ansatz for the loop-average that unifies high-momentum weak-coupling series with a stringy low-energy representation in large N Yang-Mills theory.

Findings

Derives a confining asymptote valid for large contours

Constructs a low-energy stringy theory free of ultraviolet divergences

Shows the resulting theory lacks propagating degrees of freedom at short distances

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.