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
N1 - Publisher Copyright:
© 2017, The Author(s).
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
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.
KW - Confinement
KW - Nonperturbative Effects
KW - Solitons Monopoles and Instantons
KW - Wilson’t Hooft and Polyakov loops
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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 -