Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations

Abstract

The spontaneous breaking of CP symmetry in 4D SU($N$) pure Yang-Mills theory at $\theta =\pi$ has recently attracted much attention in the context of the higher-form symmetry and the 't Hooft anomaly matching condition. Here we use Monte Carlo simulations to study the $N=2$ case, which is interesting since it is the case opposite to the large-$N$ limit, where explicit calculations are available. In order to circumvent the severe sign problem due to the $\theta$ term for real $\theta$, we first obtain results at imaginary $\theta$, where the sign problem is absent, and make an analytic continuation to real $\theta$. We use the stout smearing in defining the $\theta$ term in the action to be used in our simulations. Thus we obtain the expectation value of the topological charge and the deconfining temperature at $\theta =\pi$, and provide an evidence that the CP symmetry, which is spontaneously broken at low temperature, gets restored \emph{strictly above} the deconfining temperature. This conclusion is consistent with the anomaly matching condition and yet differs from the prediction in the large-$N$ limit.

25 pages, 9 figures; (v2) typos corrected; (v3) references added; (v4) the version accepted for publication in JHEP

References in corpus (18)

• Generalized Global Symmetries
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Tensor renormalization group and the volume independence in 2D U($N$) and SU($N$) gauge theories
• Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class
• Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• Peeking into the $\theta$ vacuum
• Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory
• Is $N=2$ Large?
• Massive Schwinger model at finite $\theta$
• Global Symmetries and Partial Confinement
• Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta =\pi$ term
• Topological features of the deconfinement transition
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• $\theta$ dependence of $T_c$ in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large $N$ limit
• Reduced tensor network formulation for non-Abelian gauge theories in arbitrary dimensions
• Absence of strong CP violation

Cited by in corpus (3)

• Generalized symmetry enriched criticality in (3+1)d
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model
• Grassmann tensor renormalization group for the massive Schwinger model with a $\theta$ term using staggered fermions