### Abstract

We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂP ^{N − 1} sigma model on ℝ×S ^{1} with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the ℂP ^{N − 1} quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon.

Original language | English |
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Article number | 190 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2019 Feb 1 |

### Keywords

- Nonperturbative Effects
- Renormalization Regularization and Renormalons
- Sigma Models

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

^{N − 1}models

*Journal of High Energy Physics*,

*2019*(2), [190]. https://doi.org/10.1007/JHEP02(2019)190