String structure of the master field of U(∞) Yang-Mills

Abstract

We argue that the internal symmetry space of the U(∞) pure Yang-Mills theory must be a functional space, actually the space of configurations of a string, in contrast with the case of the O(∞) 2-dimensional non-linear sigma-model, where it is only momentum space. We then show that the old dual-resonance model provides explicit ansätze for the classical Yang-Mills master field which is to be used to evaluate all gauge-invariant quantities; these ansätze automatically give rise to a Lorentz-invariant area-law behavior for the Wilson loop.