Is $N=2$ Large?

Abstract

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.

35 pages, 13 figures; v2: published version

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• Generalized Global Symmetries
• Pure Natural Inflation
• Topological Lattice Actions
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• $\theta =\pi$ in $SU(N)/{\mathbb{Z}}_N$ gauge theories
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• Improved thermodynamics of SU(2) gauge theory
• Small Instantons in $C{P}^1$ and $C{P}^2$ Sigma Models
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Cited by in corpus (8)

• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• $\theta$ dependence of $T_c$ in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large $N$ limit
• Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations
• Generalized symmetry constraints on deformed 4d (S)CFTs
• First-order CP phase transition in two-flavor QCD at $\theta =\pi$ under electromagnetic scale anomaly via a Nambu-Jona-Lasinio description
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model
• Generalized symmetry enriched criticality in (3+1)d