論文

査読有り 本文へのリンクあり
2019年9月20日

Renormalon structure in compactified spacetime

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

2020
1
開始ページ
013B01
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/ptz147

We point out that the location of renormalon singularities in theory on a
circle-compactified spacetime $\mathbb{R}^{d-1} \times S^1$ (with a small
radius $R \Lambda \ll 1$) can differ from that on the non-compactified
spacetime $\mathbb{R}^d$. We argue this under the following assumptions, which
are often realized in large $N$ theories with twisted boundary conditions: (i)
a loop integrand of a renormalon diagram is volume independent, i.e. it is not
modified by the compactification, and (ii) the loop momentum variable along the
$S^1$ direction is not associated with the twisted boundary conditions and
takes the values $n/R$ with integer $n$. We find that the Borel singularity is
generally shifted by $-1/2$ in the Borel $u$-plane, where the renormalon
ambiguity of $\mathcal{O}(\Lambda^k)$ is changed to
$\mathcal{O}(\Lambda^{k-1}/R)$ due to the circle compactification $\mathbb{R}^d
\to \mathbb{R}^{d-1} \times S^1$. The result is general for any dimension $d$
and is independent of details of the quantities under consideration. As an
example, we study the $\mathbb{C} P^{N-1}$ model on $\mathbb{R} \times S^1$
with $\mathbb{Z}_N$ twisted boundary conditions in the large $N$ limit.

リンク情報
DOI
https://doi.org/10.1093/ptep/ptz147
arXiv
http://arxiv.org/abs/arXiv:1909.09579
Arxiv Url
http://arxiv.org/abs/1909.09579v3
Arxiv Url
http://arxiv.org/pdf/1909.09579v3 本文へのリンクあり