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Confinement versus asymptotic freedom

High Energy Physics - Theory 2016-09-06 v1

Abstract

I put forward the low-energy confining asymptote of the solution <WC><W_{C}> (valid for large macroscopic contours C of the size >>1/ΛQCD>>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 NN\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/σph<<1/{\sqrt{\sigma_{ph}}}, where σph(ΛQCD)2\sigma_{ph}\sim{(\Lambda_{QCD})^{2}} is the physical string tension.

Keywords

Cite

@article{arxiv.hep-th/0203059,
  title  = {Confinement versus asymptotic freedom},
  author = {Andrey Yu. Dubin},
  journal= {arXiv preprint arXiv:hep-th/0203059},
  year   = {2016}
}

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13 pages