Is N=2 Large?

We study theta dependence of the vacuum energy for the 4d SU(2) pure Yang-Mills theory by lattice numerical simulations. The response of topological excitations to the smearing procedure is investigated in detail, in order to extract topological information from smeared gauge configurations. We determine the first two coefficients in the theta expansion of the vacuum energy, the topological susceptibility chi and the first dimensionless coefficient b(2), in the continuum limit. We find consistency of the SU(2) results with the large N scaling. By analytic continuing the number of colors, N , to non-integer values, we infer the phase diagram of the vacuum structure of SU(N) gauge theory as a function of N and theta. Based on the numerical results, we provide quantitative evidence that 4d SU(2) Yang-Mills theory at theta = pi is gapped with spontaneous breaking of the CP symmetry.

Automated summary

In this study, the theta dependence of vacuum energy for the 4d SU(2) pure Yang-Mills theory is investigated, with the determination of the first two coefficients in the theta expansion of the vacuum energy in the continuum limit. The SU(2) results are found to be consistent with large N scaling, and by analytic continuing the number of colors to non-integer values, the phase diagram of the vacuum structure of SU(N) gauge theory is inferred. Quantitative evidence is provided for the gapped property of 4d SU(2) Yang-Mills theory at theta = pi with spontaneous breaking of the CP symmetry based on numerical results.