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.).

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 -