The Stringy Representation of the D>=3 Yang-Mills Theory

TL;DR

This paper proposes a stringy representation for the strong coupling expansion of Wilson loop averages in D>=3 Yang-Mills theory, providing a confining solution and exploring implications for low-energy and large N limits.

Contribution

It introduces a stringy representation of the strong coupling expansion in Yang-Mills theory that satisfies the loop equations and discusses its relevance to confinement and the AdS/CFT correspondence.

Findings

Provides a confining solution to the Dyson-Schwinger equations.

Suggests a stringy pattern for the low-energy limit of D=4 Yang-Mills theory.

Discusses potential applicability of AdS/CFT to large N pure YM_{4}.

Abstract

I put forward the stringy representation of the 1/N strong coupling (SC) expansion for the regularized Wilson's loop-averages in the continuous D>=3 Yang-Mills theory (YM_{D}) with a sufficiently large bare coupling constant \lambda>\lambda_{cr} and a fixed ultraviolet cut off \Lambda. The proposed representation is proved to provide with the confining solution of the Dyson-Schwinger chain of the judiciously regularized U(N) Loop equations. Building on the results obtained, we suggest the stringy pattern of the low-energy theory associated to the D=4 U(\infty)=SU(\infty) gauge theory in the standard \lambda=>0 phase with the asymptotic freedom in the UV domain. A nontrivial test, to clarify whether the AdS/CFT correspondence conjecture may be indeed applicable to the large N pure YM_{4} theory in the \lambda=>\infty limit, is also discussed.