The stringy representation of the D⩾3 Yang–Mills theory

I continue the analysis of the stringy representation of the 1/N strong coupling (SC) expansion for the regularized Wilsonʹs loop-averages in the continuous D⩾3 Yang–Mills theory (YMD) with a sufficiently large bare coupling constant λ>λcr and a fixed ultraviolet cut off Λ. To complete the discussion of [6], we concentrate on the extreme SC regime of λ→∞ when the amplitude of the flux-tubeʹs fluctuations is vanishing compared to the flux-tubeʹs width. It is proved that, in the considered regime, the proposed representation provides with the confining solution of the judiciously regularized U(N) Loop equations. A nontrivial test, to clarify whether the AdS/CFT correspondence conjecture may be indeed applicable to the large N pure YM4 theory in the λ→∞ limit, is also discussed.