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arXiv · 2102.08784

Peeking into the $θ$ vacuum

Ryuichiro Kitano·Ryutaro Matsudo·Norikazu Yamada·Masahito Yamazaki
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Abstract

We propose a subvolume method to study the $θ$ dependence of the free energy density of the four-dimensional SU($N$) Yang-Mills theory on the lattice. As an attempt, the method is first applied to SU(2) Yang-Mills theory at $T=1.2\,T_c$ to understand the systematics of the method. We then proceed to the calculation of the vacuum energy density and obtain the $θ$ dependence qualitatively different from the high temperature case. The numerical results combined with the theoretical requirements provide the evidence for the spontaneous CP violation at $θ= π$, which is in accordance with the large $N$ prediction and indicates that the similarity between 4d SU($N$) and 2d CP$^{N-1}$ theories does not hold for $N$=2.

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Ryuichiro Kitano, Ryutaro Matsudo, Norikazu Yamada, Masahito Yamazaki. 2021-10-06. Peeking into the $θ$ vacuum. https://doi.org/10.1016/j.physletb.2021.136657

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