Fermionization, Convergent Perturbation Theory, and Correlations in the Yang-Mills Quantum Field Theory in Four Dimensions
Abstract
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|-2 - 2 dG, 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 = dimSU(n) - dimS(U(n-1) × U(1)), so that the rate of decay of correlations increases as n ∞.