Topology and universality in four dimensions

Abstract

The topological susceptibility $\chi$ is calculated for mixed-action (fundamental-adjoint) SU(2) lattice gauge theory in four dimensions. As expected, the low-order perturbative $\beta$ function does not fit the data when ${\beta }_a$ is sufficiently negative. However, the dimensionless quantity $\frac{{\sigma }^2}{\chi }$ ($\sigma$ is the string tension) is constant in the entire scaling region. This verifies universality near the crossover and the validity of the definition we use for the topological charge on the lattice.