Smooth gauge strings and D≥2 lattice Yang-Mills theories

Employing the nonabelian duality transformation [A. Dubin, hep-th/9910264], I derive the gauge string form of certain D≥3 lattice Yang-Mills (YMD) theories in the strong coupling (SC) phase. With the judicious choice of the actions, in D≥3 our construction generalizes the Gross-Taylor stringy reformulation of the continuous YM2 on a 2d manifold. Using the Eguchi-Kawai model as an example, we develop the algorithm to determine the weights w[M-tilde] for connected YM-flux worldsheets M-tilde immersed into the 2d skeleton of a D≥3 base-lattice. Owing to the invariance of w[M-tilde] under a continuous group of area-preserving worldsheet homeomorphisms, the set of weights {w[M-tilde]} can be used to define the theory of the smooth YM-fluxes which unambiguously refers to a particular continuous YMD system. I argue that the latter YMD models (with a finite ultraviolet cut-off) for sufficiently large coupling constant(s) are reproduced, to all orders in 1/N, by the smooth gauge string thus associated. The asserted YMD/String duality allows to make a concrete prediction for the 'bare' string tension σ0 which implies that (in the large N SC regime) the continuous YMD systems exhibit confinement for D≥2. The resulting pattern is qualitatively consistent (in the extreme D=4 SC limit) with the Witten's proposal motivated by the AdS/CFT correspondence