Theta dependence of the vacuum energy in the SU(3) gauge theory from the lattice

Abstract

We report on a precise computation of the topological charge distribution in the SU(3) Yang--Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the definition of the topological charge suggested by Neuberger's fermions. We observe significant deviations from a Gaussian distribution. Our results disfavour the theta behaviour of the vacuum energy predicted by instanton models, while they are compatible with the expectation from the large Nc expansion.

Figures (2)

• Figure 1: Number of configurations vs the topological charge for the lattice ${\rm A}_2$. To guide the eye, lines connect the values of the fitted distributions: the simple Gaussian (Norm), the instanton prediction in Eq. (\ref{['eq:pnuinst']}) (Inst) and the Edgeworth expansion in Eq. (\ref{['eq:pnuege']}) (Edge). The plots on right are a blowup of the top and the bottom of the distribution.
• Figure 2: Ratio of the first two cumulants vs the lattice spacing.