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
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\begin{document}$$ E(x,y) \sim |x - y|^{-2 - 2 d_G}, $$\end{document}for \documentclass[12pt]{minimal}
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\begin{document}$${|x-y|\gg 0}$$\end{document}, where dG is a positive integer depending on the gauge group G. In the case where G = SU(N), we conjecture that
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\begin{document}$$ d_G = {\rm dim}\;SU(N) - {\rm dim}\;S(U(N-1) \times U(1)), $$\end{document}so that the rate of decay of correlations increases as N → ∞.
