ON THE VALUE AND ORIGIN OF THE CHIRAL CONDENSATE IN QUENCHED SU(2) LATTICE GAUGE-THEORY

We present results of a numerical calculation of the chiral condensate in quenched SU(2) lattice gauge theory. The calculation proceeds by evaluating the spectral density distribution function for small eigenvalues on both the original lattice and after a factor-of-two blocking. It is performed on lattices as large as 204 and for couplings as small as β = 4/g2 = 2.6. The fitted values of the condensate as a function of β show good evidence for scaling and universality when compared with string tension measurements at the same value. At the smallest lattice spacings considered, we find evidence that a separation of length scales between ultraviolet fluctuations and those responsible for chiral symmetry breaking has occurred. A more qualitative study yields a significant correlation between the small modes |n〉 responsible for the non-zero value of 〈ψψ〉 and topological activity as revealed by the expectation value 〈n|γ5 ⊗ 1|n〉, and hence provides evidence for a topological origin of chiral symmetry breaking. Our interpretation is supported by a subsidiary calculation of the topological susceptibility of the vacuum. © 1990.