TY - JOUR
T1 - Infrared renormalon in the supersymmetric ℂPN-1 model on ℝ × S1
AU - Ishikawa, Kosuke
AU - Morikawa, Okuto
AU - Nakayama, Akira
AU - Shibata, Kazuya
AU - Suzuki, Hiroshi
AU - Takaura, Hiromasa
N1 - Funding Information:
Discussions with Toshiaki Fujimori, Nobuyuki Ishibashi, Tatsuhiro Misumi, Norisuke Sakai, and especially Kazuya Yonekura at the YITP workshop “Strings and Fields 2018” motivated the present work. This work was supported by Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research Grant Numbers JP18J20935 (O.M.), JP16H03982 (H.S.), and JP19K14711 (H.T.).
Publisher Copyright:
© 2020 The Author(s).
PY - 2020/2/28
Y1 - 2020/2/28
N2 - 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 ℂPN-1 model on ℝ × S1 with the ℤN twisted boundary conditions. In our large-N limit, the combination ΛR, where Λ is the dynamical scale and R is the S1 radius, is kept fixed (we set ΛR ≪ 1 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 ℝ × S1, we find that the Borel singularity at u = 2, which exists in the system on the uncompactified ℝ2 and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at u = 3/2 for the compactified space ℝ × S1. 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 ℝ × S1 prompts reconsideration on the semi-classical bion picture of the infrared renormalon.
AB - 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 ℂPN-1 model on ℝ × S1 with the ℤN twisted boundary conditions. In our large-N limit, the combination ΛR, where Λ is the dynamical scale and R is the S1 radius, is kept fixed (we set ΛR ≪ 1 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 ℝ × S1, we find that the Borel singularity at u = 2, which exists in the system on the uncompactified ℝ2 and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at u = 3/2 for the compactified space ℝ × S1. 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 ℝ × S1 prompts reconsideration on the semi-classical bion picture of the infrared renormalon.
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U2 - 10.1093/ptep/ptaa002
DO - 10.1093/ptep/ptaa002
M3 - Article
AN - SCOPUS:85082103139
VL - 2020
JO - Progress of Theoretical and Experimental Physics
JF - Progress of Theoretical and Experimental Physics
SN - 2050-3911
IS - 2
M1 - 023B10
ER -