English

Peeking into the $\theta$ vacuum

High Energy Physics - Lattice 2021-10-07 v3 High Energy Physics - Phenomenology High Energy Physics - Theory

Abstract

We propose a subvolume method to study the θ\theta dependence of the free energy density of the four-dimensional SU(NN) Yang-Mills theory on the lattice. As an attempt, the method is first applied to SU(2) Yang-Mills theory at T=1.2TcT=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\theta 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\theta = \pi, which is in accordance with the large NN prediction and indicates that the similarity between 4d SU(NN) and 2d CPN1^{N-1} theories does not hold for NN=2.

Keywords

Cite

@article{arxiv.2102.08784,
  title  = {Peeking into the $\theta$ vacuum},
  author = {Ryuichiro Kitano and Ryutaro Matsudo and Norikazu Yamada and Masahito Yamazaki},
  journal= {arXiv preprint arXiv:2102.08784},
  year   = {2021}
}

Comments

6 pages, 8 figures, text clarified, references added, systematic errors estimated, argument on surface tension omitted, Fig.7 added to clarify the limitation of the method, no significant change in conclusion. published version

R2 v1 2026-06-23T23:14:58.504Z