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.

arXiv comment35 pages, 13 figures; v2: published version

References in corpus (45)

• Generalized Global Symmetries
• Theta, Time Reversal, and Temperature
• Theta Dependence In The Large N Limit Of Four-Dimensional Gauge Theories
• SU(N) gauge theories in four dimensions: exploring the approach to N = infinity
• The high temperature phase transition in SU(N) gauge theories
• Theta dependence of SU(N) gauge theories
• Topology of the SU(2) vacuum: a lattice study using improved cooling
• Meron-Cluster Simulation of the $\theta$-Vacuum in the 2-d $O(3)$-Model
• Comparison of the gradient flow with cooling in $SU(3)$ pure gauge theory
• Theta dependence, sign problems and topological interference
• Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
• Quintessence Axion Potential Induced by Electroweak Instanton Effects
• Topological Structure in the SU(2) Vacuum
• Change of theta dependence in 4D SU(N) gauge theories across the deconfinement transition
• Axion monodromy in a model of holographic gluodynamics
• From 4d Yang-Mills to 2d ${\mathbb{CP}}^{N-1}$ model: IR problem and confinement at weak coupling
• Topological charge using cooling and the gradient flow
• Instantons and the fixed point topological charge in the two-dimensional O(3) sigma-model
• Pure Natural Inflation
• Topological Lattice Actions
• Topology at zero and finite T in SU(2) Yang-Mills theory
• Study of CP(N-1) θ-Vacua by Cluster-Simulation of SU(N) Quantum Spin Ladders
• New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and ${\mathbb{CP}}^{\mathrm{N}-1}$ Sigma Model
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Relating 't Hooft Anomalies of 4d Pure Yang-Mills and 2d ${\mathbb{CP}}^{N-1}$ Model
• Quintessence Axion Revisited in Light of Swampland Conjectures
• $\theta =\pi$ in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• Coherent Topological Charge Structure in $C{P}^{N-1}$ Models and QCD
• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
• CP(N-1) Models with Theta Term and Fixed Point Action
• Heating and small-size instantons in the $O(3)\sigma$ model on the lattice
• Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model
• First-principle simulations of 1+1d quantum field theories at $\theta =\pi$ and spin-chains
• Improved thermodynamics of SU(2) gauge theory
• Tensor Modes in Pure Natural Inflation
• Renormalization group flow and fixed point of the lattice topological charge in the 2-d O(3) sigma-model
• Theta-vacuum: Phase Transitions and/or Symmetry Breaking at $\theta =\pi$
• Electroweak Instantons, Axions, and the Cosmological Constant
• Small Instantons in $C{P}^1$ and $C{P}^2$ Sigma Models
• Density of states approach for lattice gauge theory with a $\theta$-term
• Fractionally charged Wilson loops as a probe of $\theta$-dependence in $C{P}^{N-1}$ sigma models: Instantons vs. large N
• Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus
• $\theta$-dependence in the small-$N$ limit of $2d$ $C{P}^{N-1}$ models
• Topological Susceptibility of the 2d O(3) Model under Gradient Flow
• Topological charge and cooling scales in pure SU(2) lattice gauge theory

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• 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