### Abstract

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 ℂP^{N-1} model on ℝ × S^{1} with the ℤ_{N} twisted boundary conditions. In our large-N limit, the combination ΛR, where Λ is the dynamical scale and R is the S^{1} 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 × S^{1}, we find that the Borel singularity at u = 2, which exists in the system on the uncompactified ℝ^{2} and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at u = 3/2 for the compactified space ℝ × S^{1}. 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 × S^{1} prompts reconsideration on the semi-classical bion picture of the infrared renormalon.

Original language | English |
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Article number | 023B10 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2020 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 28 2020 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

^{N-1}model on ℝ × S

^{1}.

*Progress of Theoretical and Experimental Physics*,

*2020*(2), [023B10]. https://doi.org/10.1093/ptep/ptaa002