2019年8月1日

# Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$

PTEP
• Kosuke Ishikawa
• ,
• Okuto Morikawa
• ,
• Akira Nakayama
• ,
• Kazuya Shibata
• ,
• Hiroshi Suzuki
• ,
• Hiromasa Takaura

2020
2

023B10

DOI
10.1093/ptep/ptaa002

In the leading order of the large-$N$ approximation, we study the renormalon
ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D
supersymmetric $\mathbb{C}P^{N-1}$ model on~$\mathbb{R}\times S^1$ with the
$\mathbb{Z}_N$ twisted boundary conditions. In our large~$N$ limit, the
combination $\Lambda R$, where $\Lambda$ is the dynamical scale and $R$~is the
$S^1$ radius, is kept fixed (we set $\Lambda R\ll1$ so that the perturbative
expansion with respect to the coupling constant at the mass scale~$1/R$ is
meaningful). We extract the perturbative part from the large-$N$ expression of
the gluon condensate and obtain the corresponding Borel transform~$B(u)$.
For~$\mathbb{R}\times S^1$, we find that the Borel singularity at~$u=2$, which
exists in the system on the uncompactified~$\mathbb{R}^2$ and corresponds to
twice the minimal bion action, disappears. Instead, an unfamiliar renormalon
singularity \emph{emerges\/} at~$u=3/2$ for the compactified
space~$\mathbb{R}\times S^1$. The semi-classical interpretation of this
peculiar singularity is not clear because $u=3/2$ is not dividable by the
minimal bion action. It appears that our observation for the system
on~$\mathbb{R}\times S^1$ prompts reconsideration on the semi-classical bion
picture of the infrared renormalon.

リンク情報
DOI
https://doi.org/10.1093/ptep/ptaa002
arXiv
http://arxiv.org/abs/arXiv:1908.00373
Arxiv Url
http://arxiv.org/abs/1908.00373v4
Arxiv Url
http://arxiv.org/pdf/1908.00373v4 本文へのリンクあり