Continuum QCD₂ In Terms of Discrete Random Surfaces with Local Weights

Abstract

The 1/N expansion of pure U(N) gauge theory on a two-dimensional manifold M is reformulated as the topological expansion of a special model of random surfaces defined on a lattice L covering M. The random surfaces represent branched coverings of L. The Boltzmann weight of each surface is exp[-area] times a product of local factors associated with the branch points. The 1/N corrections are produced by surfaces with higher topology as well as by contact interactions due to microscopic tubes, trousers, handles, etc. The continuum limit of this model is the limit of infinitely dense covering lattice L. The construction generalizes trivially to D > 2 where it describes the strong coupling phase of the lattice gauge theory. A possible integration measure in the space of continuous surfaces is suggested.