The properties of the SU(N) lattice gauge theory are investigated at strong coupling (λ ≃ ∞). We use a Euclidean formulation with naive fermions which preserves all the chiral symmetries of the continuum theory, and solve the theory exactly in the limit N → ∞, λ → ∞. It is shown how the hopping parameter expansion in the inverse quark mass can be summed to all orders. This method of resummation is first applied to a calculation of the order parameter of chiral symmetry, < Ψ̅ Ψ >. We compute the first two terms in the strong coupling expansion for this quantity but neglect internal fermion loops, and show that at sufficiently strong coupling, the chiral symmetry spontaneously breaks. After considering several mechanisms, we conclude that chiral symmetries break when the gauge forces are strong enough to make a quark-anti-quark bound state.
Next, we use the resummation to find the spectrum of the N = λ = ∞ theory as a function of the bare mass of the quarks, and calculate the first correction in λ-1 to this spectrum. The mesons are pseudo-Gold stone bosons, and the baryons acquire masses of order N through the spontaneous breakdown of chiral symmetry. These calculations also determine the spectrum of the strongly coupled theory at finite N in the approximation of no internal quark loops. We compare these masses to those from numerical simulations and experiment.
