### 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 |
---|---|

Article number | 190 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2019 Feb 1 |

### Fingerprint

### Keywords

- Nonperturbative Effects
- Renormalization Regularization and Renormalons
- Sigma Models

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

^{N − 1}models

*Journal of High Energy Physics*,

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

**
Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP
^{N − 1}
models
.** / Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke.

Research output: Contribution to journal › Article

^{N − 1}models ',

*Journal of High Energy Physics*, vol. 2019, no. 2, 190. https://doi.org/10.1007/JHEP02(2019)190

^{N − 1}models Journal of High Energy Physics. 2019 Feb 1;2019(2). 190. https://doi.org/10.1007/JHEP02(2019)190

}

TY - JOUR

T1 - Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 models

AU - Fujimori, Toshiaki

AU - Kamata, Syo

AU - Misumi, Tatsuhiro

AU - Nitta, Muneto

AU - Sakai, Norisuke

PY - 2019/2/1

Y1 - 2019/2/1

N2 - 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.

AB - 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.

KW - Nonperturbative Effects

KW - Renormalization Regularization and Renormalons

KW - Sigma Models

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U2 - 10.1007/JHEP02(2019)190

DO - 10.1007/JHEP02(2019)190

M3 - Article

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 2

M1 - 190

ER -