Fermionization, Convergent Perturbation Theory, and Correlations in the Yang-mills Quantum Field Theory in Four Dimensions

We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this perturbation expansion, the correlation function E(x, y) of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture will behave as E(x, y) ∼ |x− y|G , for |x− y| >> 0, where dG is a positive integer depending on the gauge group G. In the case where G = SU(n), we conjecture that dG = dim SU(n)− dim S(U(n− 1)× U(1)), so that the rate of decay of correlations increases as n→∞.