Smooth gauge strings and D≥2 lattice Yang–Mills theories Original Research Article

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[M̃] for connected YM-flux worldsheets M̃ immersed into the 2d skeleton of a D≥3 base-lattice. Owing to the invariance of w[M̃] under a continuous group of area-preserving worldsheet homeomorphisms, the set of weights {w[M̃]} 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 `bareʹ 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 Wittenʹs proposal motivated by the AdS/CFT correspondence.