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

Toshiaki Fujimori, Syo Kamata, Tatsuhiro Misumi, Muneto Nitta, Norisuke Sakai

研究成果: Article査読

34 被引用数 (Scopus)


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.

ジャーナルJournal of High Energy Physics
出版ステータスPublished - 2019 2月 1

ASJC Scopus subject areas

  • 核物理学および高エネルギー物理学


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