The coherent state variational algorithm: A numerical method for solving large-N gauge theories

This paper presents a new approach for studying large-N gauge theories which directly exploits the classical nature of the N → ∞ limit. This method supplies a practical algorithm for computing and minimizing the classical hamiltonian (or effective action) which governs N = ∞ dynamics, and allows one to calculate physical quantities such as the mass spectrum or scattering amplitudes of glueballs or mesons. Two different implementations of the basic ideas are discussed; one variant provides an algorithm for constructing N = ∞ master field matrices, while the other works directly with a list of expectation values of physical operators. Algorithms are developed for both the hamiltonian and euclidean formulations of lattice gauge theories. The inclusion of fermions in the hamiltonian version is also described. Detailed tests of the method in the context of the exactly solvable one-plaquette model are presented.