Complete integration of U(N) lattice gauge theory in a large-N limit

Itzhak Bars, Institute for Advanced Study
Frederic Green, Yale University

Abstract

We present an approximation for the integration over a link in the Feynman path integral for U(N) lattice quantum chromodynamics (QCD). The approximation is valid when N and g2N is fixed to a large value. The result is such that subsequent link integrations have the same form, allowing a complete evaluation of the path integral in any dimension over the entire lattice by repeated application of the approximation. Our technique can be applied to a variety of problems. As sources for the Yang-Mills field we use quarks traveling on world lines. We present a complete action formulation of Dirac particles on world lines with spin, color, flavor, and mass interacting with the gluon field. Evaluating the meson propagator in such a theory in our approximation we arrive at a previously proposed string model with quarks at the ends, thus demonstrating the dynamical equivalence of strings and QCD in our limit, on the lattice. © 1979 The American Physical Society.