Is N = 2 Large?

Abstract

We study θ 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 θ expansion of the vacuum energy, the topological susceptibility χ and the first dimensionless coefficient b2, 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 θ. Based on the numerical results, we provide quantitative evidence that 4d SU(2) Yang-Mills theory at θ = π is gapped with spontaneous breaking of the CP symmetry.

Large-N SU(N) Yang-Mills theories with milder topological freezing

“…We however explicitly note that the accuracy is still not high enough to exclude possible unconventional scenarios like the one put-forward in ref. [74], or to better investigate if critical corrections emerge at small N [75].…”

The Large $N_c$ limit of QCD on the lattice

“…The large-N c topological susceptibity has also been studied through the θ-dependence in Refs. [118][119][120], and in lower dimensional theories in Refs. [121,122].…”

Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing

“…We however explicitly note that the accuracy is still not high enough to exclude possible unconventional scenarios like the one put-forward in Ref. [74], or to better investigate if critical corrections emerge at small N [75].…”