### 抄録

We study four-dimensional SU(N) Yang-Mills theory on ℝ×T3=ℝ×SA1×SB1×SC1, with a twisted boundary condition by a ℤ_{N} center symmetry imposed on S_{B} ^{1} × S_{C} ^{1}. This setup has no IR zero modes and hence is free from IR divergences which could spoil trans-series expansion for physical observables. Moreover, we show that the center symmetry is preserved at weak coupling regime. This is shown by first reducing the theory on T^{2}= S_{A}× S_{B} , to connect the model to the two-dimensional ℂℙ^{N− 1}-model. Then, we prove that the twisted boundary condition by the center symmetry for the Yang-Mills is reduced to the twisted boundary condition by the ℤ_{N} global symmetry of ℂℙ^{N− 1}. There are N classical vacua, and fractional instantons connecting those N vacua dynamically restore the center symmetry. We also point out the presence of singularities on the Borel plane which depend on the shape of the compactification manifold, and comment on its implications.

元の言語 | 英語 |
---|---|

記事番号 | 88 |

ジャーナル | Journal of High Energy Physics |

巻 | 2017 |

発行部数 | 7 |

DOI | |

出版物ステータス | 出版済み - 7 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### これを引用

^{N − 1}model: IR problem and confinement at weak coupling.

*Journal of High Energy Physics*,

*2017*(7), [88]. https://doi.org/10.1007/JHEP07(2017)088

**From 4d Yang-Mills to 2d ℂℙ ^{N − 1} model : IR problem and confinement at weak coupling.** / Yamazaki, Masahito; Yonekura, Kazuya.

研究成果: ジャーナルへの寄稿 › 記事

^{N − 1}model: IR problem and confinement at weak coupling',

*Journal of High Energy Physics*, 巻. 2017, 番号 7, 88. https://doi.org/10.1007/JHEP07(2017)088

^{N − 1}model: IR problem and confinement at weak coupling. Journal of High Energy Physics. 2017 7 1;2017(7). 88. https://doi.org/10.1007/JHEP07(2017)088

}

TY - JOUR

T1 - From 4d Yang-Mills to 2d ℂℙN − 1 model

T2 - IR problem and confinement at weak coupling

AU - Yamazaki, Masahito

AU - Yonekura, Kazuya

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We study four-dimensional SU(N) Yang-Mills theory on ℝ×T3=ℝ×SA1×SB1×SC1, with a twisted boundary condition by a ℤN center symmetry imposed on SB 1 × SC 1. This setup has no IR zero modes and hence is free from IR divergences which could spoil trans-series expansion for physical observables. Moreover, we show that the center symmetry is preserved at weak coupling regime. This is shown by first reducing the theory on T2= SA× SB , to connect the model to the two-dimensional ℂℙN− 1-model. Then, we prove that the twisted boundary condition by the center symmetry for the Yang-Mills is reduced to the twisted boundary condition by the ℤN global symmetry of ℂℙN− 1. There are N classical vacua, and fractional instantons connecting those N vacua dynamically restore the center symmetry. We also point out the presence of singularities on the Borel plane which depend on the shape of the compactification manifold, and comment on its implications.

AB - We study four-dimensional SU(N) Yang-Mills theory on ℝ×T3=ℝ×SA1×SB1×SC1, with a twisted boundary condition by a ℤN center symmetry imposed on SB 1 × SC 1. This setup has no IR zero modes and hence is free from IR divergences which could spoil trans-series expansion for physical observables. Moreover, we show that the center symmetry is preserved at weak coupling regime. This is shown by first reducing the theory on T2= SA× SB , to connect the model to the two-dimensional ℂℙN− 1-model. Then, we prove that the twisted boundary condition by the center symmetry for the Yang-Mills is reduced to the twisted boundary condition by the ℤN global symmetry of ℂℙN− 1. There are N classical vacua, and fractional instantons connecting those N vacua dynamically restore the center symmetry. We also point out the presence of singularities on the Borel plane which depend on the shape of the compactification manifold, and comment on its implications.

UR - http://www.scopus.com/inward/record.url?scp=85025129813&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85025129813&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2017)088

DO - 10.1007/JHEP07(2017)088

M3 - Article

AN - SCOPUS:85025129813

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 88

ER -