2020年1月21日
Vacuum energy of the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion
PTEP
- ,
- ,
- ,
- 巻
- 2020
- 号
- 6
- 開始ページ
- 063B02
- 終了ページ
- 記述言語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1093/ptep/ptaa066
By employing the $1/N$ expansion, we compute the vacuum
energy~$E(\delta\epsilon)$ of the two-dimensional supersymmetric (SUSY)
$\mathbb{C}P^{N-1}$ model on~$\mathbb{R}\times S^1$ with $\mathbb{Z}_N$ twisted
boundary conditions to the second order in a SUSY-breaking
parameter~$\delta\epsilon$. This quantity was vigorously studied recently by
Fujimori et\ al.\ using a semi-classical approximation based on the bion,
motivated by a possible semi-classical picture on the infrared renormalon. In
our calculation, we find that the parameter~$\delta\epsilon$ receives
renormalization and, after this renormalization, the vacuum energy becomes
ultraviolet finite. To the next-to-leading order of the $1/N$ expansion, we
find that the vacuum energy normalized by the radius of the~$S^1$, $R$,
$RE(\delta\epsilon)$ behaves as inverse powers of~$\Lambda R$ for~$\Lambda R$
small, where $\Lambda$ is the dynamical scale. Since $\Lambda$ is related to
the renormalized 't~Hooft coupling~$\lambda_R$ as~$\Lambda\sim
e^{-2\pi/\lambda_R}$, to the order of the $1/N$ expansion we work out, the
vacuum energy is a purely non-perturbative quantity and has no well-defined
weak coupling expansion in~$\lambda_R$.
energy~$E(\delta\epsilon)$ of the two-dimensional supersymmetric (SUSY)
$\mathbb{C}P^{N-1}$ model on~$\mathbb{R}\times S^1$ with $\mathbb{Z}_N$ twisted
boundary conditions to the second order in a SUSY-breaking
parameter~$\delta\epsilon$. This quantity was vigorously studied recently by
Fujimori et\ al.\ using a semi-classical approximation based on the bion,
motivated by a possible semi-classical picture on the infrared renormalon. In
our calculation, we find that the parameter~$\delta\epsilon$ receives
renormalization and, after this renormalization, the vacuum energy becomes
ultraviolet finite. To the next-to-leading order of the $1/N$ expansion, we
find that the vacuum energy normalized by the radius of the~$S^1$, $R$,
$RE(\delta\epsilon)$ behaves as inverse powers of~$\Lambda R$ for~$\Lambda R$
small, where $\Lambda$ is the dynamical scale. Since $\Lambda$ is related to
the renormalized 't~Hooft coupling~$\lambda_R$ as~$\Lambda\sim
e^{-2\pi/\lambda_R}$, to the order of the $1/N$ expansion we work out, the
vacuum energy is a purely non-perturbative quantity and has no well-defined
weak coupling expansion in~$\lambda_R$.
- リンク情報
-
- DOI
- https://doi.org/10.1093/ptep/ptaa066
- arXiv
- http://arxiv.org/abs/arXiv:2001.07302
- Arxiv Url
- http://arxiv.org/abs/2001.07302v2
- Arxiv Url
- http://arxiv.org/pdf/2001.07302v2 本文へのリンクあり
- Scopus
- https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85089135513&origin=inward 本文へのリンクあり
- Scopus Citedby
- https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85089135513&origin=inward
- ID情報
-
- DOI : 10.1093/ptep/ptaa066
- eISSN : 2050-3911
- arXiv ID : arXiv:2001.07302
- SCOPUS ID : 85089135513